This phase II trial studies the effect of nivolumab in treating patients with solid tumors that have spread to other places in the body (metastatic) or cannot be removed by surgery (unresectable) with RID1A mutation and CXCL13 expression. Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving nivolumab may help to control the disease.

PRIMARY OBJECTIVES:

I. To estimate objective response rate (ORR) and overall survival (OS) in patients with ARID1A mutations receiving nivolumab therapy.

II. To estimate objective response rate (ORR) and overall survival (OS) in patients with ARID1A mutations plus CXCL13-high expression and ARID1A mutations plus CXCL13-low expression, receiving nivolumab therapy.

SECONDARY OBJECTIVES:

I. To estimate progression free survival (PFS) in subjects with harboring ARID1A mutation treated with nivolumab monotherapy.

II. To estimate progression free survival (PFS) in subjects with ARID1A mutations plus CXCL13-high expression and ARID1A mutations plus CXCL13-low expression, treated with nivolumab monotherapy.

III. To assess peripheral and tumor infiltrating immune cell sub-populations in patients with ARID1A mutations, ARID1A plus CXCL13-high and ARID1A plus CXCL13-low expression, to determine predictors of response and resistance.

IV. To determine expression pattern of CXCL13 in ARID1A mutant tumors.

OUTLINE:

Patients receive nivolumab and relatlimab IV over 30 minutes on day 1 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients undergo computed tomography (CT) or magnetic resonance imaging (MRI), tissue biopsy and blood sample collection during screening and on the trial.

Inclusion Criteria:

• Patient will have a tumor harboring genomic mutation of ARID1A
• Histological or cytological evidence of metastatic or surgically unresectable disease harboring ARID1A mutation
• All subjects must have measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria
• Evaluable tumor tissue (archived or new biopsy) must be provided for biomarker analysis as formalin-fixed paraffin-embedded (FFPE) tumor block or minimum of 10 slides. Archived tissue may be from prior biopsy of unresectable or metastatic disease or from prior surgical resection
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1
• Prior palliative radiotherapy must have been completed at least 2 weeks prior to study drug administration. Patients must have measurable disease outside the radiation field to be eligible. Patients with progression in a previously radiated field will also be eligible
• White blood cell (WBC) >= 2000/uL (obtained within 7 days prior to first dose)
• Neutrophils >= 1500/uL (obtained within 7 days prior to first dose)
• Platelets >= 100 x 1 x 10^3/uL (obtained within 7 days prior to first dose)
• Hemoglobin >= 9.0 g/dL (obtained within 7 days prior to first dose)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 x upper limit of normal (ULN) (or =< 5 X ULN for participants with liver metastases) (obtained within 7 days prior to first dose)
• Total bilirubin =< 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin < 3.0 mg/dL) (obtained within 7 days prior to first dose)
• Serum creatinine =< 1.5 x ULN or creatinine clearance (CrCl) >= 30 mL/min (using the Cockcroft-Gault formula) (obtained within 7 days prior to first dose)
• Re-enrollment: This study permits the re-enrollment of a subject that has discontinued the study as a pre-treatment failure (ie, subject has not been treated). If re-enrolled, the subject must be re-consented and inclusion/exclusion criteria reassessed
• Patients are required to participate in PA13-0291 for correlative studies. Patients will need to consent for biopsy and peripheral blood collection as documented in the study calendar
• Patients must be ≥18 years of age at enrollment.

Exclusion Criteria:

• Prior treatment with an anti-PD-1, anti-PD-L1, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways
• Active brain metastases or leptomeningeal metastases. Subjects with brain metastases are eligible if these have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for at least 4 weeks after treatment is complete and within 28 days prior to first dose of study drug administration. Where MRI is contraindicated CT scan is acceptable. Cases must be discussed with the medical monitor. Brain lesions are not considered measurable disease. There must also be no requirement for immunosuppressive doses of systemic corticosteroids (> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration
• Any serious or uncontrolled medical disorder, that in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results
• Prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, prostate cancer without evidence of prostate specific antigen (PSA) progression or carcinoma in situ such as the following: gastric, prostate, cervix, colon, melanoma, or breast for example
• Subjects with active, known or suspected autoimmune disease. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism, due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll
• Subjects with a condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease
• All toxicities attributed to prior anti-cancer therapy other than neuropathy, alopecia and fatigue must have resolved to grade 1 (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] version 5) or baseline before administration of study drug. Subjects with toxicities attributed to prior anti-cancer therapy which are not expected to resolve and result in long lasting sequelae, such as neuropathy after platinum based therapy, are permitted to enroll. Neuropathy must have resolved to grade 2 (NCI CTCAE version 5)
• Treatment with any chemotherapy, radiation therapy, biologics for cancer, or investigational therapy within 28 days of first administration of study treatment. Prior palliative radiotherapy must have been completed at least 2 weeks prior to study drug administration as indicated in inclusion criteria
• Positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (RNA) or hepatitis C antibody (HCV antibody) indicating acute or chronic infection
• Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS)
• Patients that are pregnant or lactating.