• Pharmacokinetics (PK): Minimum Concentration (Cmin) of LY3434172 [ Time Frame: Predose Cycle 1 Day 1 through Cycle 4 Day 1 (Up to 42 Day Cycle) ]
  PK: Cmin of LY3434172
• Objective Response Rate (ORR): Percentage of Participants with a Complete Response (CR) or Partial Response (PR) [ Time Frame: Baseline through Measured Progressive Disease (Estimated up to 12 Months) ]
  ORR: Percentage of participants with a CR or PR
• Duration of Response (DOR) [ Time Frame: Date of CR or PR to Date of Objective Progression or Death Due to Any Cause (Estimated up to 12 Months) ]
  DOR
• Time to Response (TTR) [ Time Frame: Baseline to Date of CR or PR (Estimated up to 12 Months) ]
  TTR
• Disease Control Rate (DCR): Percentage of Participants who Exhibit Stable Disease (SD), CR or PR [ Time Frame: Baseline through Measured Progressive Disease (Estimated up to 12 Months) ]
  DCR: Percentage of participants who exhibit SD, CR or PR

Inclusion Criteria:

• Must have histological or cytological evidence of a diagnosis of cancer that is not amenable/resistant to approved standard-of-care therapy for the following solid tumors: Melanoma, non-small cell lung cancer (NSCLC), squamous cell carcinoma of the head and neck (SCCHN), urothelial cancer, gastric cancer, colorectal cancer, biliary tract cancer, anal cancer, nasopharyngeal cancer, esophageal cancer, SCLC, ovarian cancer, mesothelioma, pan-tumor MSIhi solid tumors, hepatocellular carcinoma, merkel cell cancer, cutaneous squamous cell carcinoma, endometrial cancer, breast cancer, cervical cancer, thyroid cancer, salivary cancer, and prostate cancer who have received at least one line of standard systemic therapy for their respective tumor type in the metastatic setting with progressive locally advanced or metastatic disease. Prior anti-programmed death 1 (PD-1) and anti-programmed death ligand 1 (PD-L1) allowed if they received another therapy immediately prior to this study or there has been a lapse of approximately ≥90 days from prior therapy.
• Must be willing to undergo pretreatment and on-treatment core needle or excisional tumor biopsies.
• Have at least one measurable lesion assessable as defined by the Response Evaluation Criteria in Solid Tumors (RECIST) 1.1.
• Have adequate organ function.
• Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) scale.
• Have an estimated life expectancy of 12 weeks, in the judgment of the investigator.

Exclusion Criteria:

• Have symptomatic central nervous system (CNS) malignancy or metastasis not requiring concurrent treatment, including but not limited to surgery, radiation, corticosteroids and/or anticonvulsants to treat CNS metastases, and their disease is asymptomatic and radiographically stable for at least 30 days.
• Have moderate or severe cardiovascular disease.
• Have active or suspected autoimmune disease (eg. autoimmune vasculitis, autoimmune myocarditis, among others).

• Have serious concomitant systemic disorder that would compromise the participant's ability to adhere to the protocol, including known infection with human immunodeficiency virus (HIV) unless they are well controlled on highly active antiretroviral therapy (HAART) therapy with no evidence of acquired immune deficiency syndrome (AIDS)-defining opportunistic infections within the last 2 years, and CD4 T-cells count > 350 cells/µl , active hepatitis B virus (HBV), active hepatitis C virus (HCV), active autoimmune disorders, or prior documented severe autoimmune or inflammatory disorders requiring immunosuppressive treatment.

  • Use of escalating or chronic supraphysiologic doses of corticosteroids or immunosuppressive agents (such as, exceeding 10 milligrams/day of prednisone or equivalent). Use of topical, ophthalmic, inhaled, and intranasal corticosteroids permitted.
• Bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection, Crohn's disease, ulcerative colitis, or chronic diarrhea.
• Evidence of interstitial lung disease or noninfectious pneumonitis (active or treated by corticosteroid therapy).