Study of Pembrolizumab Following Surgery in Patients With Microsatellite Instability High (MSI-H) Solid Tumors

Inclusion Criteria: * Age 18 years or older * ECOG performance status 0-1 * Any solid tumor with MSI or MRD by IHC, PCR or NGS testing. MSKCC confirmation of MSI-H/MRD status is not mandatory prior to enrollment and treatment on the study. For patients with outside testing, if sufficient tissue is available NGS will be repeated at MSKCC and will not impact the patient's eligibility. * Must have genetic testing of DNA from primary tumor for somatic genomic alterations across a minimum of 50 genes. * Must have undergone a complete curative surgical resection (R0) * Must have completed standard of care (SOC) surgery, neoadjuvant or adjuvant therapy * To be eligible for pembrolizumab or placebo therapy, the patients must have positive ctDNA (as defined in section 7.0) within 4 months after completion of appropriate standard of care therapy (surgery, chemotherapy, radiation as appropriate). Note, if ctDNA has a negative result, ctDNA can be re-tested up to 3 months later, within 9 months of completion of standard therapy. * Patients must sign informed consent within 4 weeks of positive ctDNA result. The 4 weeks is considered from the date that the ctDNA is resulted, and not the date it is drawn. * Demonstrate adequate organ function: * Absolute neutrophil count (ANC) ≥1,500 /mcL * Platelets ≥100,000 / mcL * Hemoglobin ≥9 g/dL * Serum creatinine ≤1.5 X upper limit of normal (ULN) * Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN. Except patients with Gilbert's disease (≤3x ULN) * AST and ALT ≤ 2.5 X ULN * Albumin ≥3 mg/dL Exclusion Criteria: * Patients who have not recovered from serious adverse events (as determined by treating MD) related to surgery. * Presence of metastatic or recurrent disease. * Had R1 ( microscopic residual tumor) or R2 resection (macroscopic residual tumor at resection margin). * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., dexamethasone containing antiemetic regimen or steroids as CT scan contrast premedication) may be enrolled. * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. * Has a known history of active TB (Bacillus tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. o Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-CTLA-4 agent. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease; systemic lupus erythematosus; Wegener syndrome \[granulomatosis with polyangiitis\]; myasthenia gravis; Graves' disease; rheumatoid arthritis, hypophysitis, uveitis) within the past 3 years prior to the start of treatment. The following are exceptions to this criterion: * Subjects with vitiligo or alopecia * Subjects with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement or psoriasis not requiring systemic treatment. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy. o Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. * Is unwilling to give written informed consent, unwillingness to participate, or inability to comply with the protocol for the duration of the study.