This screening and multi-sub-study randomized phase II/III trial will establish a method for genomic screening of similar large cancer populations followed by assigning and accruing simultaneously to a multi-sub-study hybrid ?Master Protocol? (S1400). The type of cancer trait (biomarker) will determine to which sub-study, within this protocol, a participant will be assigned to compare new targeted cancer therapy, designed to block the growth and spread of cancer, or combinations to standard of care therapy with the ultimate goal of being able to approve new targeted therapies in this setting. In addition, the protocol includes a ?non-match? sub-study which will include all screened patients not eligible for any of the biomarker-driven sub-studies. This sub-study will compare a non-match therapy to standard of care also with the goal of approval.

PRIMARY OBJECTIVES:

Screening component:

I. To establish a National Clinical Trials Network (NCTN) mechanism for genomically screening large but homogeneous cancer populations and subsequently assigning and accruing simultaneously to a multi-sub-study ?Master Protocol.? II. To evaluate the screen success rate defined as the percentage of screened patients that register for a therapeutic sub-study.

Sub-study-specific Objectives:

Design #1: Phase II/III Design:

III. To evaluate if there is sufficient evidence to continue to the Phase III component of the sub-study by comparing investigator-assessed progression-free survival (IA-PFS) between investigational therapy versus standard therapy (SoC) in patients with advanced stage refractory squamous cell carcinoma (SCCA) of the lung. (Phase II) IV. To determine if there is both a statistically and clinically-meaningful difference in IA-PFS among advanced stage refractory SCCA of the lung randomized to receive investigational therapy versus SoC. (Phase III) V. To compare overall survival (OS) in patients with advanced stage refractory SCCA of the lung randomized to investigational therapy versus SoC. (Phase III)

Design #2: Phase II followed by Phase III (Sequential Phase II to Phase III):

VI. To evaluate the objective response rate (confirmed and unconfirmed, complete and partial). (Phase II) VII. To determine if there is both a statistically and clinically-meaningful difference in IA-PFS among advanced stage refractory SCCA of the lung randomized to receive investigational therapy versus SoC. (Phase III) VIII. To compare overall survival (OS) in patients with advanced stage refractory SCCA of the lung randomized to investigational therapy versus SoC. (Phase III)

SECONDARY OBJECTIVES:

Sub-study-specific Objectives:

Design #1: Phase II/III Design:

I. To compare response rates (confirmed and unconfirmed, complete and partial responses) among patients randomized to receive investigational therapy versus SoC. (Phase II) II. To evaluate the frequency and severity of toxicities associated with investigational therapy versus SoC. (Phase II) III. To evaluate the duration of response (DoR) among patients who achieve a complete response (CR) or a partial response (PR) by Response Evaluation Criteria in Solid Tumors (RECIST) (1.1). (Phase II) III. To compare the response rates (confirmed and unconfirmed, complete and partial) among patients randomized to receive investigational therapy versus SoC. (Phase III) IV. To evaluate the frequency and severity of toxicities associated with investigational therapy versus SoC. (Phase III)

Design #2: Phase II followed by Phase III (Sequential Phase II to Phase III):

V. To evaluate PFS and OS with investigational therapy. (Phase II) VI. To evaluate the DoR among patients who achieve a CR or PR (confirmed and unconfirmed) by RECIST 1.1. (Phase II) VII. To evaluate the frequency and severity of toxicities associated with investigational therapy. (Phase II) VIII. To compare the response rates (confirmed and unconfirmed, complete and partial) among patients randomized to receive investigational therapy versus SoC. (Phase III) IX. To evaluate the frequency and severity of toxicities associated with investigational therapy versus SoC. (Phase III)

TERTIARY OBJECTIVES:

I. To evaluate the treatment arm randomization acceptance rate (TARAR) within each treatment arm of each sub-study defined as the percentage of patients randomized to a treatment arm that receive any protocol treatment. (Design #1: Phase II/III Design) II. To identify additional predictive tumor/blood biomarkers that may modify response or define resistance to the targeted therapy (TT)/targeted therapy combination (TTC) beyond the chosen biomarker for biomarker-driven sub-studies.

III. To evaluate potentially predictive biomarkers for non-match therapy (NMT) in the non-match studies.

IV. To identify potential resistance biomarkers at disease progression. V. To establish a tissue/ blood repository from patients with refractory SCCA of the lung.

OUTLINE: Patients are assigned to a biomarker-driven targeted therapy phase II study. If the objectives response rate observed is judged sufficient, patients proceed to a randomized phase III trial and are randomized to biomarker-driven targeted therapy or standard of care.

S1400A: (CLOSED TO ACCRUAL 12/18/2015) Patients with tumors that do not match one of the currently active drug-biomarker combinations or did not meet the eligibility requirements for that bio-marker driven sub-study are assigned to Arm I. Upon evidence of progression following discontinuation of 12 months of treatment, patients may restart treatment for up to 12 months with the same treatment guidelines followed during the initial 12-month treatment period (Arm III).

ARM I: (CLOSED TO ACCRUAL 12/18/2015) Patients receive anti-B7H1 monoclonal antibody MEDI4736 intravenously (IV) over 60 minutes on day 1. Treatment repeats every 14 days for 12 months in the absence of disease progression or unacceptable toxicity.

ARM II (CLOSED TO ACCRUAL 4/2015): Patients receive docetaxel IV on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. (closed to accrual with Revision #2 4/22/15)

ARM III: For patients assigned to Arm 1, MEDI4736: Upon evidence of progression following discontinuation of 12 months of treatment, patients may restart treatment with Arm 3, MEDI4736 for up to 12 months with the same treatment guidelines followed during the initial 12-month treatment period. Patients will only be able to restart treatment once; thus a maximum of two 12-month periods will be allowed. Patients receive anti-B7H1 monoclonal antibody MEDI4736 intravenously (IV) over 60 minutes on day 1. Treatment repeats every 14 days for 12 months in the absence of disease progression or unacceptable toxicity.

S1400B (CLOSED TO ACCRUAL 12/12/2016): Patients with tumors positive for phosphoinositide 3-kinase (PI3KCA) are assigned to Arm I. Patients currently on Arm 2, docetaxel will be given the option to re-register to Arm 3, GCD-0032 after disease progression on current treatment (Arm III).

ARM I: Patients receive taselisib orally (PO) daily on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

ARM II (CLOSED TO ACCRUAL 12/18/2015): Patients receive docetaxel IV on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. (closed to accrual with Revision #3 12/18/2015)

ARM III: Re-Registration Treatment with GDC-0032 (Taselisib) Upon progression patients in Arm 2 may be eligible for Re-Registration to receive GDC-0032. Patients receive taselisib orally (PO) daily on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

S1400C (CLOSED TO ACCRUAL 09/01/2016): Patients with tumors positive for cyclin dependent kinase 4 (CDK4), cyclin D1 (CCND1), cyclin D2 (CCND2), and cyclin D3 (CCND3) are assigned to Arm I. Patients currently on Arm 2, docetaxel will be given the option to re-register to Arm 3, palbociclib, after disease progression on current treatment (Arm III).

ARM I: Patients receive palbociclib PO on days 1-21. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM II (CLOSED TO ACCRUAL 12/18/2015): Patients receive docetaxel IV on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. (closed to accrual with Revision #3 12/18/2015)

ARM III: Re-Registration Treatment with Palbociclib. Upon progression patients in Arm 2 may be eligible for Re-Registration to receive palbociclib. Patients receive palbociclib PO on days 1-21. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

S1400D (CLOSED TO ACCRUAL 10/31/2016): Patients with tumors positive for fibroblast growth factor receptor (FGFR) 1, FGFR2, and FGFR3 are assigned to Arm I. Patients currently on Arm 2, docetaxel will be given the option to re-register to Arm 3, AZD4547, after disease progression on current treatment (Arm III).

ARM I: Patients receive FGFR inhibitor AZD4547 PO BID on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

ARM II (CLOSED TO ACCRUAL 12/18/2015): Patients receive docetaxel IV on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. (closed to accrual with Revision #3 12/18/2015)

ARM III: Re-Registration Treatment with AZD4547. Upon progression patients in Arm 2 may be eligible for Re-Registration to receive AZD4547. Patients receive FGFR inhibitor AZD4547 PO BID on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

S1400E (CLOSED TO ACCRUAL 11/25/2014): Patients with tumors positive for met proto-oncogene (MET) are randomized to 1 of 2 treatment arms. (permanently closed to accrual on 11/25/14)

ARM I: Patients receive rilotumumab IV on day 1 and erlotinib hydrochloride PO daily on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

ARM II: Patients receive erlotinib hydrochloride PO daily on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

S1400F: Patients with disease progression during or after prior anti-PD-1 or anti-PD-L1 antibody monotherapy as their most recent line of treatment receive durvalumab (IV over 60 minutes) and tremelimumab (IV over 60 minutes) on day 1 for courses 1-4 and durvalumab IV alone on day 1 of course 5 and subsequent courses until disease progression or unacceptable toxicity. Courses repeat every 28 days.

S1400G: Patients with tumors positive for homologous recombination repair deficiency receive talazoparib PO daily on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

S1400I: Patients with tumors that do not match one of the currently active drug-biomarker combinations or did not meet the eligibility requirements for that bio-marker driven sub-study are randomized to 1 of 2 treatment arms.

ARM I: Patients receive nivolumab IV over 30 minutes on day 1 and ipilimumab IV over 60 minutes on day 1 of every third course. Courses repeat every 14 days in the absence of disease progression or unacceptable toxicity.

ARM II: Patients receive nivolumab IV over 30 minutes on day 1. Courses repeat every 14 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, all patients are followed up periodically for up to 3 years from date of screening registration.

Inclusion Criteria:

• SCREENING/PRE-SCREENING REGISTRATION:

• Patients must have pathologically proven squamous cell carcinoma (SCCA) cancer of the lung confirmed by tumor biopsy and/or fine-needle aspiration; disease must be stage IV SCCA, or recurrent; the primary diagnosis of SCCA should be established using the current World Health Organization (WHO)/International Association for the Study of Lung Cancer (IASLC)-classification of Thoracic Malignancies; the diagnosis is based on hematoxylin and eosin (H&E) stained slides with or without specific defined immunohistochemistry (IHC) characteristic (p40/p63 positive, transcription termination factor [TTF1] negative) if required for diagnosis; mixed histologies are not allowed

• Patients must either be eligible to be screened at progression on prior treatment or to be pre-screened prior to progression on current treatment; patients will either consent to the screening consent or the pre-screening consent, not both; these criteria are:

  • Screening at progression on prior treatment: to be eligible for screening at progression, patients must have received at least one line of systemic therapy for any stage of disease (stages I-IV) and must have progressed during or following their most recent line of therapy; for patients whose prior systemic therapy was for stage I-III disease only (i.e. patient has not received any treatment for stage IV or recurrent disease), the prior systemic therapy must have been a platinum-based chemotherapy regimen and disease progression on the platinum-based chemotherapy must have occurred within one year from the last date that patient received that therapy; for patients whose prior therapy was for stage IV or recurrent disease, the patient must have received at least one line of a platinum-based chemotherapy regimen or checkpoint inhibitor therapy (e.g. nivolumab or pembrolizumab)
  • Pre-screening prior to progression on current treatment: to be eligible for pre-screening, current treatment must be for stage IV or recurrent disease and patient must have received at least one dose of the current regimen; patients must have previously received or currently be receiving a platinum-based chemotherapy regimen or checkpoint inhibitor therapy (e.g. nivolumab or pembrolizumab); patients on first-line platinum-based treatment are eligible upon receiving cycle 1, day 1 infusion; Note: patients will not receive their sub-study assignment until they progress and the S1400 Notice of Progression is submitted

• Patients must have adequate tumor tissue available, defined as >= 20% tumor cells and >= 0.2 mm^3 tumor volume

  • The local interpreting pathologist must review the specimen
  • The pathologist must sign the S1400 Local Pathology Review Form confirming tissue adequacy prior to screening/pre-screening registration
  • Patients must agree to have this tissue submitted to Foundation Medicine for common broad platform Clinical Laboratory Improvement Act (CLIA) biomarker profiling; if archival tumor material is exhausted, then a new fresh tumor biopsy that is formalin-fixed and paraffin-embedded (FFPE) must be obtained; a tumor block or FFPE slides 4-5 microns thick must be submitted; bone biopsies are not allowed; if FFPE slides are to be submitted, at least 12 unstained slides plus an H&E stained slide, or 13 unstained slides must be submitted; however it is strongly recommended that 20 FFPE slides be submitted; Note: previous next-generation deoxyribonucleic acid (DNA) sequencing (NGS) will be repeated if done outside this study for sub-study assignment; patients must agree to have any tissue that remains after NGS testing retained for the use of the translational medicine (TM) studies (if such TM studies are defined) within any sub-study the patient is enrolled in

• Patients must not have a known epidermal growth factor receptor (EGFR) mutation or anaplastic lymphoma kinase (ALK) fusion; EGFR/ALK testing is not required prior to registration and is included in the Foundation Medicine Incorporated (FMI) testing for screening/prescreening

• Patients must have Zubrod performance status 0-1 documented within 28 days prior to screening/pre-screening registration

• Patients must also be offered participation in banking for future use of specimens

• Patients must be willing to provide prior smoking history as required on the S1400 Onstudy Form

• As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system

• Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines

• SUB-STUDY REGISTRATION:

• Patients whose biomarker profiling results indicate the presence of an EGFR mutation or echinoderm microtubule-associated protein-like 4 (EML4)/ALK fusion are not eligible

• Patients must have progressed (in the opinion of the treating investigator) following the most recent line of therapy

• Patients must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to sub-study registration; patients must have recovered (=< grade 1) from any side effects of prior therapy; patients must not have received any radiation therapy within 14 days prior to sub-study registration

• Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI); the CT from a combined positron emission tomography (PET)/CT may be used to document only non-measurable disease unless it is of diagnostic quality; measurable disease must be assessed within 28 days prior to sub-study registration; pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease; non-measurable disease must be assessed within 42 days prior to sub-study registration; all disease must be assessed and documented on the Baseline Tumor Assessment Form; patients whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to registration

• Patients must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study registration; patient must not have leptomeningeal disease, spinal cord compression or brain metastases unless: (1) metastases have been locally treated and have remained clinically controlled and asymptomatic for at least 14 days following treatment and prior to registration, AND (2) patient has no residual neurological dysfunction and has been off corticosteroids for at least 24 hours prior to sub-study registration

• Patient must have fully recovered from the effects of prior surgery at least 14 days prior to sub-study registration

• Patients must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment; concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable

• Absolute neutrophil count (ANC) >= 1,500/mcl obtained within 28 days prior to sub-study registration

• Platelet count >= 100,000 mcl obtained within 28 days prior to sub-study registration

• Hemoglobin >= 9 g/dL obtained within 28 days prior to sub-study registration

• Serum bilirubin =< institutional upper limit of normal (IULN) within 28 days prior to sub-study registration; for patients with liver metastases, bilirubin must be =< 5 x IULN

• Either alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =< 2 x IULN within 28 days prior to sub-study registration (if both ALT and AST are done, both must be =< 2 IULN); for patients with liver metastases, either ALT or AST must be =< 5 x IULN (if both ALT and AST are done, both must be =< 5 x IULN)

• Serum creatinine =< the IULN OR measured or calculated creatinine clearance >= 50 mL/min using the following Cockcroft-Gault Formula within 28 days prior to sub-study registration

• Patients must have Zubrod performance status 0-1 documented within 28 days prior to sub-study registration

• Patients must not have any grade III/IV cardiac disease as defined by the New York Heart Association Criteria (i.e., patients with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within 6 months, or serious uncontrolled cardiac arrhythmia

• Patients must not have documented evidence of acute hepatitis or have an active or uncontrolled infection

• Patients with a known history of human immunodeficiency virus (HIV) seropositivity:

  • Must have undetectable viral load using standard HIV assays in clinical practice
  • Must have cluster of differentiation (CD)4 count >= 400/mcL
  • Must not require prophylaxis for any opportunistic infections (i.e., fungal, Mycobacterium avium complex [mAC], or pneumocystis jiroveci pneumonia [PCP] prophylaxis)
  • Must not be newly diagnosed within 12 months prior to sub-study registration

• Prestudy history and physical exam must be obtained within 28 days prior to sub-study registration

• No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years

• Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures

• As part of the OPEN registration process the treating institution?s identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the system

• Patients with impaired decision-making capacity are eligible as long as their neurological or psychological condition does not preclude their safe participation in the study (e.g., tracking pill consumption and reporting adverse events to the investigator)

• Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines.

Patients must have pathologically proven squamous cell carcinoma (SCCA) cancer of the lung confirmed by tumor biopsy and/or fine-needle aspiration; disease must be stage IV SCCA, or recurrent; the primary diagnosis of SCCA should be established using the current World Health Organization (WHO)/International Association for the Study of Lung Cancer (IASLC)-classification of Thoracic Malignancies; the diagnosis is based on hematoxylin and eosin (H&E) stained slides with or without specific defined immunohistochemistry (IHC) characteristic (p40/p63 positive, transcription termination factor [TTF1] negative) if required for diagnosis; mixed histologies are not allowed