This research study is studying a combination of a targeted therapy and an immune therapy as a possible treatment.

The drugs involved in this study are:

• Prexasertib (LY2606368)
• LY3300054

This research study is a Phase I clinical trial, which tests the safety of an investigational drug and also tries to define the appropriate doses of the investigational drugs to use for further studies. "Investigational" means that the drugs are being studied.

The FDA (the U.S. Food and Drug Administration) has not approved prexasertib or LY3300054 as a treatment for any disease.

Prexasertib (LY2606368) is a checkpoint kinase 1 (CHK1) inhibitor that is being developed as a treatment for patients with advanced cancer. CHK1 inhibitors work by preventing the cancer cells from being able to repair damaged DNA (one of the building blocks of a cell) which then leads to cell death.

A monoclonal antibody is a protein that is made in a laboratory that can target specific substances in the body. LY3300054 is a monoclonal antibody that targets programmed cell death ligand 1 (PD-L1). PD-L1 is a protein often produced by cancer cells or surrounding cells that stops white blood cells from attacking the cancer cells. The drug blocks the protein, allowing the immune system to recognize and attack the cancer cells.

Inclusion Criteria:

• Written informed consent obtained prior to any study-specific procedures not considered part of routine medical care.

• Patients must have histologically confirmed solid tumor that is metastatic or unresectable, and there is no available therapy likely to convey clinical benefit

• Patients must have measurable disease by RECIST version 1.1. Measurable disease is defined as at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥ 20mm (≥ 2cm) with conventional techniques or as ≥ 10mm (≥ 1cm) with spiral computed tomography (CT) scan, MRI, or calipers by clinical exam. See Section 11 for the evaluation of measurable disease.

• Patients must have recovered to eligibility levels from prior toxicity or adverse events as a result of previous treatment prior to entering the study (except alopecia).

• Age ≥18 years, as no dosing or adverse event data are currently available on the use of prexasertib in combination with LY3300054 in patients < 18 years of age, children are excluded from this study.

• ECOG performance status 0-1.

• Patients must have normal organ and marrow function as defined below:

  • absolute neutrophil count ≥ 1,500/mcL
  • platelets ≥ 100,000/mcL
  • total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN)
  • AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional ULN
  • creatinine ≤ 1.5 × institutional ULN OR
  • creatinine clearance ≥ 60 mL/min by Cockcroft-Gault equation for participants with creatinine levels above institutional normal.
  • Free T4 within institutional normal limits

• The effects of prexasertib and LY3300054 on the developing human fetus are unknown. For this reason, women of childbearing potential and male patients with partners of childbearing potential must agree to use two highly effective forms of contraception (see Section 5.5.1) prior to study entry, for the duration of study participation, and for 6 months after completion of study. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and for 3 months after completion of prexasertib and LY3300054 administration. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

• Women of childbearing potential enrolling on study must have a negative serum pregnancy test prior to registration.

• Childbearing potential is defined as women who are not postmenopausal (defined as amenorrheic for ≥ 12 months following cessation of any exogenous hormonal treatments; LH and FSH levels in the postmenopausal range for women under 50; radiation-induced oophorectomy with last menses > 12 months prior; or chemotherapy-induced menopause with last menses > 12 months prior) or surgically sterile (bilateral oophorectomy or hysterectomy).

• Ability to understand and the willingness to sign a written informed consent document. Patients must be willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations.

Exclusion Criteria:

• Participants who have had chemotherapy, immune therapy, or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C; five-half lives for any investigational or FDA-approved kinase inhibitors) prior to entering the study. Patients who have received prior CHK1 inhibitor therapy are excluded. Exposure to prior PD-L1 antibody will be allowed as long as this was not the most recent treatment prior to enrollment.
• No prior radiation to > 25% of the marrow
• Must not have received more than 4 lines of cytotoxic chemotherapy. A line of therapy is defined as being preceded by disease progression. Discontinuation of a regimen without progression (for example, due to toxicity) or a switch of an agent within the same drug class (for example from cisplatin to carboplatin) will not be considered a new line of therapy. Similarly, maintenance therapy (continuation maintenance or switch maintenance) will not be considered a new line of treatment.
• Participants who are receiving any other investigational agents.
• Participants who have undergone major surgery within 14 days of starting the study treatment, or participants who have not recovered to baseline status from the effects of major surgery received more than 14 days prior.
• Participants with known brain metastases or carcinomatous meningitis are excluded from this clinical trial, with the exception of patients with brain metastatic disease that has previously been treated and remained stable on MRI ≥ 2 months prior to enrollment, without steroids or anti-epileptic medications. These patients may be enrolled at the discretion of the Principal Investigator.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, uncontrolled seizures, myocardial infarction within the past 3 months, superior vena cava syndrome, unstable spinal cord compression (untreated and unstable for at least 28 days prior to study entry), or psychiatric illness/social situations that would limit compliance with study requirements.
• Participants must not have experienced a Grade ≥ 3 immune-related AE or an immune-related neurologic or ocular AE of any grade while receiving prior immunotherapy, or experienced a toxicity of any grade that led to permanent discontinuation of prior immunotherapy as a result of the toxicity. Participants with prior endocrine adverse events of Grade ≤ 2 are permitted to enroll if stably maintained on appropriate replacement therapy and are asymptomatic. In the setting of prior immune-related AE, participants must not have required the use of additional immunosuppressive agents other than corticosteroids for the management of the adverse event(s), not have experienced recurrence of the adverse event if re-challenged, and not currently requiring maintenance doses of > 10 mg of prednisone or equivalent per day at the time of enrollment.
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to prexasertib or LY3300054.
• The effects of prexasertib and LY3300054 on the developing human fetus are unknown. For this reason, pregnant women are excluded from this study. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with prexasertib and LY3300054, breastfeeding women are also excluded.
• Known HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with prexasertib and LY3300054. In addition, these participants are at increased risk of lethal infections when treated with marrow-suppressive therapy such as prexasertib.
• Participants with known active or chronic infection with Hepatitis B or C.
• Consistent QTc > 470 msec on more than one screening ECG. Patients with a history of long QTc syndrome or personal or family history of ventricular arrhythmias will be excluded