Nivolumab and Ipilimumab in Mucinous Colorectal and Appendiceal Tumors

Inclusion Criteria: * Subjects must have signed and dated an IRB-approved written informed consent form prior to the performance of any protocol-related procedures that are not part of standard care. * Colorectal or appendiceal mucinous adenocarcinoma with peritoneal-only metastatic disease. It is recognized that in some patients, peritoneal disease will predominate without distinction of the site of origin, and such patients will be eligible. * Microsatellite stable by PCR and/or mismatch repair proficient by immunohistochemistry * ECOG performance status of 0 or 1 * Prior therapy with a fluoropyrimidine, oxaliplatin, and irinotecan unless contraindicated or refused. Prior treatment with antiangiogenic and/or anti-EGFR antibody therapy is permitted but not required * Measurable disease by RECIST v. 1.1 * Laboratory parameters: * Absolute neutrophil count \> 1500/μL * Platelets \> 100,000/μL * Hemoglobin \> 9.0 g/dL * PT/INR or PTT \< 1.5xULN * Creatinine \< 1.5xULN OR creatinine clearance \> 50 mL/min by Cockcroft-Gault formula * Total bilirubin \< 1.5xULN * Subjects with Gilbert's Syndrome must have a total bilirubin level of \< 3.0xULN * Albumin \> 3.0 g/dL * AST and/or ALT: \< 3.0×ULN * Subjects with HIV are permitted provided they meet the following criteria: * CD4+ cell count \> 250 cells/mm3 * No history of AIDS-defining conditions other than low CD4+ count * If subject is on antiretroviral therapy, there must not be expected significant drug-drug interactions with study treatment Exclusion Criteria: * Bowel obstruction within the past 60 days * Subjects who are currently pregnant, planning to become pregnant, or breast-feeding. * Females participants of child-bearing potential are required to use an effective contraception method or abstain from intercourse during treatment and for at least 5 months following the last dose * Males participants with partners of child-bearing potential are required to use an effective contraception method or abstain from intercourse during treatment and for at least 7 months following the last dose * Subjects who, in the opinion of the physician, would not be clinically appropriate for receipt of the therapy regimen associated with participation * Subjects with contraindications to immune checkpoint therapy, as follows: * Interstitial lung disease that is symptomatic or may interfere with the detection and management of suspected drug-related pulmonary toxicity * Prior organ allograft or allogeneic bone marrow transplantation * Pre-existing thyroid abnormality with thyroid function that cannot be maintained in the normal range with medication * Active autoimmune disease, except for vitiligo, type 1 diabetes mellitus, asthma, atopic dermatitis, or endocrinopathies manageable by hormone replacement; other autoimmune conditions may be allowable at the discretion of the principal investigator * Condition requiring systemic treatment with corticosteroids * Systemic steroids at physiologic doses (equivalent to dose of oral prednisone 10 mg) are permitted. * Intranasal, inhaled, topical, intra-articular, and ocular corticosteroids with minimal systemic absorption are permitted. * Established non-peritoneal metastatic disease, including but not limited to metastases to the liver, lung, brain, extra-abdominal lymph nodes, and bone * A second primary malignancy that, in the judgment of the investigator, may affect interpretation of results * Prior treatment with an anti-PD-1, anti-PD-L1, or anti-CTLA-4 antibody * Toxicities attributed to prior anti-cancer therapy other than alopecia, fatigue, and peripheral neuropathy must have resolved to Grade 1 or baseline before administration of study drug. In addition, a washout period will be required for prior therapies as specified: * No chemotherapy within 14 days prior to first dose * No investigational product(s) (IPs) and/or biologic therapy within 28 days or 5 half-lives, whichever is longer, prior to first dose * No major surgery within 28 days prior to first dose. Any surgery-related AE(s) must have resolved at least 14 days prior to first dose. * No radiation therapy with curative intent within 28 days prior to first dose. Prior focal palliative radiotherapy must have been completed at least 14 days prior to first dose. * Active hepatitis B or hepatitis C, defined as the following: * Hepatitis B surface antigen positive or HBV DNA PCR \>100 IU/mL * Hepatitis C antibody positive unless HCV RNA PCR is negative (i.e. undetectable viral load) * Prisoners or participants who are involuntarily incarcerated. (Note: under specific circumstances a person who has been imprisoned may be included as a participant. Strict conditions apply and BMS approval is required.) * Participants who are compulsorily detained for treatment of either a psychiatric or physical (eg, infectious disease) illness