This phase II trial studies molecular profiling-based assignment of cancer therapy (MPACT) in treating patients with solid tumors that have spread to other places in the body and usually cannot be cured or controlled with treatment (advanced). Adavosertib, everolimus, and trametinib are drugs that each target a specific variation in tumors by blocking different proteins needed for cell growth. Veliparib blocks an enzyme that helps repair deoxyribonucleic acid (DNA) damaged by chemotherapy, which may help chemotherapy drugs work better. It is not yet known whether testing patients for variations in their tumor and assigning treatment targeting the variation is more effective than standard non-targeted therapy in treating advanced solid tumors.

PRIMARY OBJECTIVE:

I. Evaluate the proportion of patients with objective response (OR) to targeted study agent(s) in patients with advanced refractory cancers.

OUTLINE: Patients are assigned to 1 of 4 treatment regimens corresponding to one of their mutation/amplification categories.

REGIMEN I: Patients receive veliparib orally (PO) twice daily (BID) on days 1-7 and temozolomide PO once daily (QD) on days 1-5. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

REGIMEN II: Patients receive adavosertib PO BID for 5 doses starting on day 1 and carboplatin intravenously (IV) over 30-60 minutes on day 1. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. (No longer an active study drug as of March 2018)

REGIMEN III: Patients receive everolimus PO every day (QD) on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. (No longer an active study drug as of March 2018)

REGIMEN IV: Patients receive trametinib PO QD on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. (No longer an active study drug as of March 2018)

After completion of study treatment, patients are followed up for 30 days. Patients with unacceptable toxicities that have not resolved by day 30 are followed up biweekly until stabilization or resolution.

Inclusion Criteria:

• TUMOR BIOPSY SEQUENCING: Patients with histologically documented solid tumors whose disease has progressed following at least one line of standard therapy and/or no standard of treatment exists that has been shown to prolong survival

• TUMOR BIOPSY SEQUENCING: Patient must have tumor amenable to percutaneous or excisional skin biopsy and be willing to undergo a tumor biopsy or biopsy samples (formalin-fixed paraffin-embedded [FFPE] blocks) collected on another study or from a procedure performed due to medical necessity may be acceptable if collected within 6 months prior to registration on molecular profiling-based assignment of cancer therapy (MPACT) and providing that the patient has not received any investigational or targeted treatment since that time, or a report from a Molecular Analysis for Therapy Choice (MATCH) study designated Clinical Laboratory Improvement Act (CLIA) laboratory that a patient has a variant in the genes of interest

• TUMOR BIOPSY SEQUENCING: Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as >= 20 mm with conventional techniques or as >= 10 mm with spiral computed tomography (CT) scan

• TUMOR BIOPSY SEQUENCING: Patients with bone metastases or hypercalcemia on intravenous bisphosphonate treatment, denosumab, or similar agents are eligible to participate and may continue this treatment; patients with prostate cancer may continue luteinizing hormone-releasing hormone (LHRH) agonists or antagonists

• TUMOR BIOPSY SEQUENCING: Karnofsky performance status >= 70%

• TUMOR BIOPSY SEQUENCING: Life expectancy > 3 months

• TUMOR BIOPSY SEQUENCING: Absolute neutrophil count >= 1,000/uL (mcL)

• TUMOR BIOPSY SEQUENCING: Platelets >= 100,000/uL (mcL)

• TUMOR BIOPSY SEQUENCING: Total bilirubin < 1.5 x institutional upper limit of normal

• TUMOR BIOPSY SEQUENCING: Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3 x institutional upper limit of normal

• TUMOR BIOPSY SEQUENCING: Creatinine < 1.5 x institutional upper limit of normal OR creatinine clearance >= 60 mL/min for patients with creatinine levels >= 1.5 x institutional upper limit of normal

• TUMOR BIOPSY SEQUENCING: The effects of these targeted agents on the developing human fetus are unknown or anticipated to cause fetal harm based on their mechanism of action; for this reason, women of childbearing potential and men must agree to use highly effective contraception prior to study entry, for the duration of study participation, and for 3 months after completion of study; because there may be a risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued while the patient is on this trial and for 30 days following last dose of study drug

• TUMOR BIOPSY SEQUENCING: Patients with history of central nervous system (CNS) metastases who have received treatment and who either have not had seizures or have been on stable doses of anti-seizure medicine and had no seizures for 4 weeks will be eligible; enzyme-inducing anticonvulsants are contraindicated

• TUMOR BIOPSY SEQUENCING: Ability to understand and the willingness to sign a written informed consent document (subjects with impaired decision-making capacity are not eligible)

• TREATMENT: Patient must have predefined targeted mutation in tumor biopsy

• TREATMENT: Patients with histologically documented solid tumors whose disease has progressed following at least one line of standard therapy or for which no standard therapy exists that has been shown to prolong survival

• TREATMENT: Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as >= 20 mm with conventional techniques or as >= 10 mm with spiral CT scan

• TREATMENT: Any prior therapy, radiotherapy, or major surgery must have been completed >= 3 weeks (> 6 weeks for nitrosoureas or mitomycin C) or 5 half-lives of the agent (whichever is shorter) prior to enrollment on protocol, and the participant must have recovered to eligibility levels from prior toxicity; radiofrequency ablation (RFA) of localized lesions should have been performed >= 2 weeks prior to treatment

• TREATMENT: Patients with bone metastases or hypercalcemia on intravenous bisphosphonate treatment, denosumab, or similar agents are eligible to participate and may continue this treatment; patients with prostate cancer may continue LHRH agonists or antagonists

• TREATMENT: Karnofsky performance status >= 70%

• TREATMENT: Absolute neutrophil count >= 1,000/uL (mcL)

• TREATMENT: Platelets >= 100,000/uL (mcL)

• TREATMENT: Total bilirubin < 1.5 x institutional upper limit of normal

• TREATMENT: AST (SGOT)/ALT (SGPT) =< 3 x institutional upper limit of normal

• TREATMENT: Creatinine < 1.5 x institutional upper limit of normal OR creatinine clearance >= 60 mL/min for patients with creatinine levels >= 1.5 x institutional upper limit of normal

• TREATMENT: Life expectancy > 3 months

• TREATMENT: The effects of these targeted agents on the developing human fetus are unknown or anticipated to cause fetal harm based on their mechanism of action; for this reason, women of childbearing potential and men must agree to use highly effective contraception (see list below) prior to study entry, for the duration of study participation, and for 3 months after completion of study;

  • Total abstinence: When this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence [e.g., calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception)
  • Sterilization: have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment
  • In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment
  • Male partner sterilization (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate); (for female subjects on the study, the vasectomized male partner should be the sole partner for that subject); use of a combination of any two of the following:
  • Use of oral, injected, implanted or other hormonal methods of contraception
  • Placement of an intrauterine device (IUD) or intrauterine system (IUS)
  • Barrier methods of contraception: Condom or Occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository
  • In case of use of oral contraception, women should have been stable on the oral agent before taking study treatment
  • Sexually active males must use a condom during intercourse

• TREATMENT: Because there may be a risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued while the patient is on this trial and for 30 days following last dose of study drug

• TREATMENT: Patients with ovarian cancer or metastatic breast cancer and breast cancer gene (BRCA) mutations must have received approved poly (ADP-ribose) polymerase (PARP) inhibitor therapy; these patients are eligible for the veliparib plus temozolomide arm unless the PARP inhibitor was administered with temozolomide

• TREATMENT: Patients with a history of seizures are not eligible to receive veliparib

• TREATMENT: Patients who have had prior treatment with any PARP inhibitor in combination with temozolomide are not eligible to receive treatment with veliparib on this study; patients who have received prior temozolomide or PARP inhibitor with or without other chemotherapy/targeted agent should not be excluded

• TREATMENT: Patients must have >= 10.0 g/dL hemoglobin (Hb) and no blood transfusion in the past 28 days to receive veliparib

Exclusion Criteria:

• TUMOR BIOPSY SEQUENCING: Women who are pregnant or breastfeeding
• TUMOR BIOPSY SEQUENCING: Patients who are receiving any other investigational agents; patients on other trials will be eligible as long as they are no longer receiving study treatment
• TUMOR BIOPSY SEQUENCING: Patients with uncontrolled intercurrent illness including, but not limited to psychiatric illness/social situations that would limit compliance with study requirements, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, myocardial infarction in the past 6 months, invasive fungal infections, or active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and active and chronic hepatitis (i.e., quantifiable hepatitis B virus [HBV]-DNA and/or positive hepatitis B surface antigen [HbsAg], quantifiable hepatitis C virus [HCV]-ribonucleic acid [RNA]) are not eligible to participate; testing for hepatitis B or other infections for eligibility will be performed only if clinically indicated
• TUMOR BIOPSY SEQUENCING: Patients with gastrointestinal conditions that might predispose for drug intolerability or poor drug absorption (e.g., inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, malabsorption syndrome, and active peptic ulcer disease) are excluded; subjects with Crohn's disease or a partial or complete small bowel obstruction are also excluded, as are any patients who cannot swallow tablets or capsules whole; tablets or capsules must not be crushed or chewed; nasogastric or gastrostomy tube (G-tube) administration is not allowed
• TUMOR BIOPSY SEQUENCING: Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic (PK) interactions
• TUMOR BIOPSY SEQUENCING: Patients who require use of coumarin-derivative anticoagulants such as warfarin are excluded; low molecular weight heparin is permitted for prophylactic or therapeutic use
• TUMOR BIOPSY SEQUENCING: Patients who have previously been treated with the combination of temozolomide plus a PARP inhibitor should not be considered eligible for a biopsy given that these patients would not be eligible for the active veliparib plus temozolomide arm
• TREATMENT: Women who are pregnant or breastfeeding
• TREATMENT: Patients who are receiving any other investigational agents; patients on other trials will be eligible as long as they are no longer receiving study treatment
• TREATMENT: Patients with active brain metastases or carcinomatous meningitis are excluded from this clinical trial; patients who have a history of seizures are not eligible to receive veliparib
• TREATMENT: Patients with uncontrolled intercurrent illness including, but not limited to psychiatric illness/social situations that would limit compliance with study requirements, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, myocardial infarction in the past 6 months, invasive fungal infections, or active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and active and chronic hepatitis (i.e., quantifiable hepatitis B virus (HBV)-DNA and/or positive hepatitis B surface antibody (HbsAg), quantifiable hepatitis C virus (HCV)-RNA) are not eligible to participate; testing for hepatitis B or other infections for eligibility will be performed only if clinically indicated
• TREATMENT: Patients with gastrointestinal conditions that might predispose for drug intolerability or poor drug absorption (e.g., inability to take oral medication or a requirement for intravenous (IV) alimentation, prior surgical procedures affecting absorption, malabsorption syndrome, and active peptic ulcer disease) are excluded; subjects with Crohn's disease or a partial or complete small bowel obstruction are also excluded, as are any patients who cannot swallow tablets or capsules whole; tablets or capsules must not be crushed or chewed; nasogastric or G-tube administration is not allowed
• TREATMENT: HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for PK interactions
• TREATMENT: Eligibility of subjects receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics (i.e., cytochrome P450, family 3, subfamily A, polypeptide 4 [CYP450], P-glycoprotein [PgP]) of any of the study drugs will be determined following review of their cases by the principal investigator (PI); patients on strong and moderate cytochrome P450 system inducers or inhibitors are ineligible; every effort would be made to switch patients off medications that are known substrates of CYP450; if it is medically important for the patient to remain on such medications, these patients can still be eligible to participate based on PI discretion
• TREATMENT: Patients who require use of coumarin-derivative anticoagulants such as warfarin are excluded; low molecular weight heparin is permitted for prophylactic or therapeutic use
• TREATMENT: Patients who have a history of another primary malignancy, with the exceptions of: non-melanoma skin cancer, and carcinoma in situ of the cervix, uteri, or breast from which the patient has been disease free for > 3 years
• TREATMENT: Patients with treatment-related acute myeloid leukemia (AML) (t-AML)/myelodysplastic syndrome (MDS), or with features suggestive of AML/MDS, or who have had prior allogeneic bone marrow transplant or double umbilical cord blood transplantation, should not receive veliparib due to reports of MDS and leukemia secondary to oncology therapy on Cancer Therapy Evaluation Program (CTEP)-sponsored studies utilizing veliparib