The purpose of this study is to evaluate the safety of the study drug known as LY3321367, an anti-T-cell immunoglobulin and mucin-domain domain-containing molecule-3 (TIM-3) antibody administered alone or in combination with LY3300054, an anti-programmed death ligand 1 (PD-L1) antibody, in participants with advanced relapsed/refractory solid tumors.

Inclusion Criteria:

• For Ph1a monotherapy and combination cohorts, histologic or cytologic confirmation of advanced solid tumor.

• For Phase 1a and 1b, prior PD-1 or PD-L1 therapy or other immunotherapy is allowed, if the following criteria are met:

  • Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy.
  • Must have completely recovered or recovered to baseline prior to screening from any prior AEs occurring while receiving prior immunotherapy.

• Must have provided tumor tissue sample, as follows:

  • For participants entering Ph1a: have submitted, if available, an archival tumor tissue sample.
  • For participants entering Ph1b: have submitted, a sample from a newly obtained core or excisional biopsy of a tumor lesion or a recent biopsy defined by 6 months of study enrollment (Ph1b).

• Must have a performance status of 0 to 1 on the Eastern Cooperative Oncology Group (ECOG) scale.

• Must have adequate organ function.

• Have an estimated life expectancy of 12 weeks, in judgement of the investigator.

Exclusion Criteria:

• Have symptomatic or uncontrolled brain metastases, spinal cord compression, or leptomeningeal disease requiring concurrent treatment, including but not limited to surgery, radiation, and/or corticosteroids (participants receiving anticonvulsants are eligible).
• Have received a live vaccine within 30 days before the first dose of study treatment.
• If female, is pregnant, breastfeeding, or planning to become pregnant.
• Have a history or current evidence of any condition, therapy, or laboratory abnormality that might interfere with the participant's participation.
• Have moderate or severe cardiovascular disease.
• Have a serious concomitant systemic disorder that would compromise the participant's ability to adhere to the protocol, including active or chronic infection with human immunodeficiency virus (HIV), 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, cyclosporine). [Use of topical, ophthalmic, inhaled, and intranasal corticosteroids permitted].
• Bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection.
• Evidence of interstitial lung disease or noninfectious pneumonitis.