M7824 in Patients With Metastatic Colorectal Cancer or With Advanced Solid Tumors With Microsatellite Instability

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma of the colon or the rectum that is metastatic or unresectable (cohorts A,B); histologically or cytologically confirmed carcinoma not originating in the colon or rectum (cohort C); or histologically or cytologically confirmed adenocarcinoma of the colon or the rectum following resection of the primary tumor and metastatic disease, following completion of standard-of-care perioperative therapy at the discretion of the treating provider (cohort D). * Confirmation of: a) Cohort A: microsatellite instability in colorectal cancer (CRC); b) Cohort B: CMS4 CRC classification on pretreatment primary tumor; c) Cohort C: microsatellite instability in non-CRC solid tumor; d. Cohort D: microsatellite stability. * Ability to provide written informed consent. * Documented progression to prior therapies (Cohorts A, B, and C): a) Cohort A: Disease progression following prior immune checkpoint blockade therapy; b) Cohort B: Progression or intolerance to at least 2 prior lines of standard therapy for unresectable or metastatic CRC; c) Cohort C: Disease progression following prior immune checkpoint blockade therapy. * Available primary tumor tissue for CMS4 biomarker assessment. * Life expectancy \>= 12 weeks as judged by the treating physician. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1(Cohorts A, B, and C). For cohort B, measureable lesions must be identified apart from the irradiated tumor lesion. Patients in cohort D must have no evidence of radiographically evident disease at the time of study entry. * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (in absence of blood transfusion). * Lymphocyte count \>= 0.5 x 10\^9/L (in absence of blood transfusion). * Platelet count \>= 100 x 10\^9/L (in absence of blood transfusion). * Hemoglobin (Hgb) \>= 9 g/dL (in absence of blood transfusion). * Total bilirubin level =\< 1.5 x the upper limit of normal (ULN). * An aspartate aminotransferase (AST) level =\< 2.5 x ULN, and an alanine aminotransferase (ALT) level =\< 2.5 x ULN. If liver metastases are present, then it is acceptable for AST level =\< 5.0 x ULN, and an ALT level =\< 5.0 x ULN. * International normalized ratio (INR) \< 1.5. * An estimated creatinine clearance \> 30 mL/min according to the Cockcroft-Gault formula or be measure for creatinine clearance from 24-hour urine collection. * Highly effective contraception for both male and female subjects if the risk of conception exists. Highly effective contraception must be used 30 days prior to first trial administration, for the duration of trial treatment, and at least for 4 months after stopping trial treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this trial, the treating physician should be informed immediately. * Ability to tolerate receipt of radiotherapy to a metastasis not adjacent to a normal dose-limiting structure, at the discretion of the treating radiation oncologist (cohort B). * Presence of detectable ctDNA following completion of R0 resection with or without perioperative therapy, with confirmation of somatic mutations in the resected tumor (cohort D only). * Completion of all standard-of-care adjuvant therapy (cohort D). Exclusion Criteria: * Concurrent treatment with non-permitted drugs and other interventions. * Anticancer treatment within 14 days before the start of trial treatment (e.g., cytoreductive therapy, radiotherapy \[with the exception of palliative radiotherapy delivered in a normal organ-sparing technique\], immune therapy, or cytokine therapy). * Major surgery as determined by the investigator within 28 days before the start of trial treatment (prior diagnostic biopsy is permitted). * Systemic therapy with immunosuppressive agents within 7 days before the start of treatment; or use of any investigational drug within 28 days before the start of trial treatment. * Cohort A and C only: Intolerance or serious adverse immune related adverse events (irAEs) that were symptomatic or required or continues to require ongoing immunosuppression to previous immune checkpoint therapy. * Cohort B and D: prior exposure to any immune checkpoint blockade agent or any other immunomodulatory agent used for antineoplastic therapy for mCRC. * Previous malignant disease (other than the target malignancy to be investigated in this trial) within 3 years prior to study treatment initiation. Subjects with a history of cervical carcinoma in situ, superficial or non-invasive bladder cancer, or basal cell or squamous cell carcinoma in situ, previously treated with curative intent are NOT excluded. Subjects with other localized malignancies treated with curative intent need to be discussed with the principal investigator. * Subjects with active central nervous system (CNS) metastases are excluded. Subjects with a history of treated CNS metastases (by surgery or radiation therapy) are not eligible unless they have fully recovered from treatment, demonstrated no progression for at least 2 months, and do not require continued steroid therapy. * Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). * Significant acute or chronic infections including, among others: a) Known history of testing positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome; b) Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (HBV surface antigen positive and HBV core antibody positive with reflex to positive HBV DNA or HBV core antibody positive alone with reflex to positive HBV DNA or positive HCV antibody with reflex to positive HCV ribonucleic acid \[RNA\]); c) Subjects with active tuberculosis (history of exposure or history of positive tuberculosis test plus presence of clinical symptoms, physical or radiographic findings). * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent: a) Subjects with type I diabetes, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible; b) Subjects requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for the purpose of hormonal replacement and at doses =\< 10 mg of prednisone or equivalent per day; c) Administration of steroids for other conditions through a route known to result in a minimal systemic exposure (topical, intranasal, intro-ocular, or inhalation) is acceptable. * Known severe hypersensitivity reactions to monoclonal antibodies (grade \>= 3 National Cancer Institute \[NCI\]-Common Terminology Criteria for Adverse Events \[CTCAE\] v4.03), any history of anaphylaxis, or recent (within 5 months) history of uncontrolled asthma. * Persisting toxicity (except alopecia and vitiligo) related to prior oncologic therapy grade \> 1 NCI-CTCAE v4.03, however, sensory neuropathy grade =\< 2 is acceptable. * Clinically significant cardiovascular/ cerebrovascular disease as follows: cerebral vascular accident / stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification class \> II), or serious cardiac arrhythmia. * Clinically relevant diseases (for example, inflammatory bowel disease) and / or uncontrolled medical conditions, which, in the opinion of the Investigator, might impair the subject's tolerance or ability to participate in the trial. * Vaccine administration within 4 weeks of M7824 administration. Vaccination with live vaccines while on trial is prohibited. Administration of inactivated vaccines is allowed (for example, inactivated influenza vaccines). * Cohort D: peritoneal carcinomatosis.