Inclusion Criteria:

          -  Patient must be >= 18 years of age

          -  Patient must have histologically confirmed adenocarcinoma of the rectum with the
             inferior margin within 15 cm from the anal verge based on colonoscopy and/or flexible
             sigmoidoscopy

          -  Patient must have T3-4Nx or TxN+ disease (stage II or III) based on magnetic resonance
             imaging of the pelvis and computed tomography of the chest and abdomen. These baseline
             scans must be done within 28 days prior to registration

          -  Patient must have MSI-H (microsatellite instability-high) or dMMR (deficient mismatch
             repair) tumors based on immunohistochemistry or PCR (polymerase chain reaction)

          -  Patient must have Eastern Cooperative Oncology Group (ECOG) Performance status 0-2

          -  Patient must have the ability to understand and the willingness to sign a written
             informed consent document. Patients with impaired decision-making capacity (IDMC) who
             have a legally authorized representative (LAR) or caregiver and/or family member
             available will also be considered eligible

          -  Patient must agree to not receive live vaccines while on this study

          -  Patients of childbearing potential and sexually active patients must not expect to
             conceive or father children by using accepted and effective method(s) of contraception
             or by abstaining from sexual intercourse for at least one month (female patients) or
             one week (male patients) prior to the start of study drug and continue for 5 months
             after the last dose of study drug (for female patients). Investigators must counsel
             patients on the importance of pregnancy prevention and the implications of an
             unexpected pregnancy

          -  Leukocytes >= 3,000/mcL (must be obtained =< 14 days prior to protocol registration)

          -  Absolute neutrophil count (ANC) >= 1,500/mcL (must be obtained =< 14 days prior to
             protocol registration)

          -  Platelets >= 100,000/mcL (must be obtained =< 14 days prior to protocol registration)

          -  Total bilirubin =< institutional upper limit of normal (ULN) (must be obtained =< 14
             days prior to protocol registration)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) =<
             2.5 x institutional ULN (must be obtained =< 14 days prior to protocol registration)

          -  Creatinine =< 1.5 x institutional ULN (must be obtained =< 14 days prior to protocol
             registration)

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months of registration are eligible for
             this trial

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable on suppressive therapy, if indicated

          -  Patients with a history of hepatitis C virus (HCV) infection must have been treated
             and cured. For patients with HCV infection who are currently on treatment, they are
             eligible if they have an undetectable HCV viral load

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class 2B or better

        Exclusion Criteria:

          -  Patient must not have previously received chemotherapy or immunotherapy for rectal
             cancer

          -  Patient must not have previously received radiotherapy to the pelvis

          -  Patient must not have had major surgery performed within 28 days prior to registration

          -  Patient must not have a history of interstitial lung disease (e.g., pneumonitis or
             pulmonary fibrosis) or evidence of interstitial lung disease on baseline chest
             computed tomography (CT) scan

          -  Patient must not have a serious active infection requiring IV antibiotics at time of
             registration

          -  Patient must not have active autoimmune disease or history of autoimmune disease that
             might recur, which may affect vital organ function or require immune suppressive
             treatment including chronic prolonged systemic corticosteroids (defined as
             corticosteroid use of duration one month or greater). These include but are not
             limited to patients with a history of immune related neurologic disease, multiple
             sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia
             gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE),
             connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's,
             ulcerative colitis, and patients with a history of toxic epidermal necrolysis (TEN),
             Stevens-Johnson syndrome, or anti-phospholipid syndrome. Patients with any of these
             are ineligible for this study because of the risk of recurrence or exacerbation of
             disease

          -  Patient must not have a condition requiring systemic treatment with either
             corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive
             medications within 14 days prior to registration. Inhaled or topical steroids and
             adrenal replacement doses < 10 mg daily prednisone equivalents are permitted in the
             absence of active autoimmune disease. Patients are permitted to use topical, ocular,
             intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic
             absorption). Physiologic replacement doses of systemic corticosteroids are permitted,
             even if < 10 mg/day prednisone equivalents. A brief course of corticosteroids for
             prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions
             (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted

          -  Patient must not be pregnant or breast-feeding due to the potential harm to an unborn
             fetus and possible risk for adverse events in nursing infants with the treatment
             regimens being used. All patients of childbearing potential must have a blood test or
             urine study within 2 weeks prior to registration to rule out pregnancy. A repeat
             pregnancy test must be done within 72 hours prior to first dose of treatment if the
             baseline test was done outside the 72 hour window. A patient of childbearing potential
             is defined as anyone, regardless of sexual orientation or whether they have undergone
             tubal ligation, who meets the following criteria: 1) has achieved menarche at some
             point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not
             been naturally postmenopausal (amenorrhea following cancer therapy does not rule out
             childbearing potential) for at least 24 consecutive months (i.e., has had menses at
             any time in the preceding 24 consecutive months)