A Trial of Regorafenib Plus Lorigerlimab in Patients With Locally Recurrent or Regrowing pMMR/MSS Localized Rectal Cancer

Inclusion Criteria: * Histological or pathological confirmation of rectal or anal adenocarcinoma (collectively referred to as "rectal cancer" or "rectal (adeno)carcinoma" throughout this protocol). * MSS or pMMR status as tested according to institutional standard practice. For example, pMMR status can be determined by intact expression by immunohistochemistry of all 4 mismatch repair proteins (MLH1, MSH2, MSH6, and PMS2) while microsatellite instability can be determined by polymerase chain reaction (PCR) or next generation sequencing (NGS). Note: methodologies (e.g., ddPCR, NGS) to determine microsatellite instability on ctDNA are acceptable for study eligibility evaluation. * The evidence of regrowth, confirmed by biopsy, following a near-complete or complete response at least three months following completion of planned total neoadjuvant therapy or locally recurrent disease after total neoadjuvant therapy as treatment for localized rectal cancer at the discretion of the treating provider or PI. * The potential for R0 (complete) resection of the residual cancer at the discretion of the surgeon must be documented. * Willing to undergo pretreatment biopsy of the regrowing or recurrent rectal cancer that can be both safely and effectively biopsied at the discretion of the collaborator. * ECOG performance status of 0 or 1 (APPENDIX A). * Ability to understand, willingness to sign a written informed consent document and compliance with the study procedures. * Ability to swallow and retain pills. * Adequate organ and marrow function within 28 days prior to registration as defined below: * absolute neutrophil count . 1.0 x 103/uL * hemoglobin . 9 g/dL * platelet count . 75 x 103/uL * total bilirubin . 1.5 x institutional upper limit of normal (ULN) * AST/ALT . 3 \~ institutional ULN. * Serum creatinine . 1.5 \~ the institutional ULN OR measured OR calculated creatinine clearance . 40 mL/min using the following Cockroft-Gault equation as follows: CrCl (mL/min) = \[(140 . age) x (weight in kg) € \[72 x (serum creatinine in mg/dL)\] \[0.85 if female\]. * Adequate cardiac function. Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants must be class 2 or better. * The effects of the combination of regorafenib and lorigerlimab on the developing human fetus are unknown. For this reason, some participants (as defined below) must be willing to use contraception (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). Female participants who are not postmenopausal (defined as having no menses for at least one year without an alternative medical cause and confirmed with high follicle-stimulating hormone level), i.e., of childbearing potential, must agree to use a highly effective contraception method (either combined estrogen and progestogen contraception, progestogen-only hormonal contraception, intrauterine device, intrauterine hormone-releasing system, or bilateral tubal occlusion, or similar). For males, they must have either undergone bilateral orchiectomy, vasectomy with medical confirmation of surgical success, or agree to use male condom if engaging in sexual activity with female of childbearing potential who uses a highly effective contraception method (either combined estrogen and progestogen contraception, progestogen-only hormonal contraception, intrauterine device, intrauterine hormone-releasing system, or bilateral tubal occlusion, or similar). A double-barrier contraceptive method (male use of condom and female use of cap, diaphragm, or sponge with spermicide) is required while on study (i.e., from time of consent) and through 7 months after last dose of both study drugs for females of childbearing potential. If a female participant has a partner with medical confirmation of surgically successful vasectomy, this can be used in lieu of the aforementioned criteria. For males engaging in sexual activity with a female of childbearing potential, contraception is required while on study (i.e., from time of consent) and through 7 months after last dose of Lorigerlimab, and 4 months after last dose of Regorafenib. Exclusion Criteria: * The presence of distant metastatic disease at the time of study screening, or a history of any distant metastatic colorectal cancer. * Re-irradiation (a second course of definitive radiation) as definitive therapy for locally recurrent disease after previous standard therapy for localized rectal cancer. * Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways. * Planned treatment with other systemic anti-cancer agents (e.g., chemotherapy, hormonal therapy, immunotherapy) or other treatments not part of protocolspecified anti-cancer therapy including concurrent investigational agents of any type. * Prior treatment with regorafenib or fruquintinib. * Treatment with any investigational drug within 30 days prior to enrollment or 5 investigational agent half-lives (whichever is longer). * An active condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of registration. Participants are permitted the use of topical, ocular, intraarticular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Replacement steroid doses \> 10 mg daily prednisone or equivalents are permitted in the absence of active autoimmune disease. A brief (less than 3 weeks) 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 a contact allergen) is permitted. * Impairment of gastrointestinal function or disease, at the discretion of the treating provider or PI, that may significantly alter the absorption of study drug (e.g., ulcerative diseases, uncontrolled vomiting, malabsorption syndrome, small bowel resection with decreased intestinal absorption). * A history of GI perforation (note: tumor-related perforation of a resected primary tumor is not applicable), GI bleeding within 4 weeks prior to study registration, or clinically significant diverticulitis or flare-up within 4 weeks prior to study registration). * A history of inflammatory bowel disease, (including ulcerative colitis and Crohn's disease), symptomatic autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's Granulomatosis\]); CNS or motor neuropathy considered of autoimmune origin (e.g., Guillain-Barre Syndrome and myasthenia gravis, multiple sclerosis). Note: participants with Graves' disease that is controlled on thyroid supplement/replacement, type 1 insulin-dependent diabetes mellitus that is controlled on insulin therapy, or any other autoimmune disease that is controlled at the discretion of the treating provider or PI while on steroid replacement therapy are allowed to participate. * A history of pneumonitis that has required oral or IV steroids within the last 12 months. * A history of a Grade 3 or 4 allergic reaction attributed to humanized or human monoclonal antibody therapy. * A history of a prior allogeneic tissue or solid organ transplant. * A history of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) within 6 months prior to study registration. * A history of myocarditis. * Persistent proteinuria of NCI-CTCAE Grade 3. Urine dipstick result of 3+ or abnormal, based on type of urine test strip used, is allowed if protein excretion (estimated by urine protein/creatinine ratio on a random urine sample) is \<3.5 g/24 hr. * History of uncontrolled intercurrent illness including but not limited to: * Uncontrolled active infection requiring antibiotics at the time of initiation of study treatment. * Uncontrolled cardiac arrythmias. * Non-healing wound or non-healing ulcer. * Major surgical procedure or significant traumatic injury within 28 days before start of study medication. If participants received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Other co-existing malignancies or previous malignant disease (other than colorectal cancer) within the last 3 years except for thyroid cancer (papillary or follicular), non-melanoma skin cancers, the following in situ cancers: bladder, gastric, colon, cervical/dysplasia, breast, or melanoma and any malignancy deemed in complete remission prior to study entry for which no additional therapy is required or anticipated to be required during the study period. * Administration of a live, attenuated vaccine within 120 days prior to start of study treatment or anticipation that such a live attenuated vaccine will be required during the study. Administration of live, attenuated vaccines is therefore prohibited during study treatment. Inactivated vaccines are allowed (for example, inactivated influenza vaccines). * Coexisting separate disease, metabolic disorder, clinically significant laboratory result, or any other condition that the treating provider or PI suspects may (a) prohibit use of the investigational product, or (b) put the patient at undue risk of harm. * Known active viral hepatitis B (i.e., HBsAg positive prior to enrollment) or hepatitis C infection. Patients with past or resolved hepatitis B virus infection (i.e., HBsAg negative, anti-HBc positive, and HBV DNA negative tests prior to enrollment) are eligible for this trial. Anti-HCV antibody positive will be eligible only if PCR is negative for HCV RNA. * Known active tuberculosis (history of exposure or history of positive TB test plus presence of clinical symptoms, physical or radiographic findings). * Known positivity to the human immunodeficiency virus (HIV) or active acquired immunodeficiency syndrome (AIDS). Patients on effective anti-retroviral therapy with undetectable viral load and CD4 count \>200/unit are eligible for this trial. * Concomitant or prior use within 2 weeks before start of study treatment of strong inhibitors and inducers of CYP3A4 activity (listed in APPENDIX B). Note: inducers and inhibitors of CYP3A4 should be avoided, or selection of an alternate concomitant medicinal product, with no or minimal potential to induce or inhibit CYP3A4, should be considered. * Therapeutic anticoagulation with Vitamin-K antagonists (e.g., warfarin) or with heparins and heparinoids. Note: prophylactic anticoagulation as follows is allowed: low dose warfarin (1 mg orally, once daily) with PT-INR . 1.5 x ULN is permitted. Infrequent bleeding or elevations in PT-INR have been reported in some subjects taking warfarin while on regorafenib therapy. Therefore, subjects taking concomitant warfarin should be monitored regularly for changes in PT, PT-INR or clinical bleeding episodes; low dose aspirin (. 100 mg daily); prophylactic doses of heparin. * Use of any herbal remedy that may unsafely interact with study drugs at the discretion of the treating provider or PI (e.g. St. John fs wort \[Hypericum perforatum\]). * Active pregnancy or nursing. Pregnant women are excluded from this study because: a) effects of regorafenib on pregnancy and lactation in humans are unknown but its use is advised against since there is preclinical evidence of reproductive toxicity and fetal harm and harm to breast-fed children cannot be excluded; b) reproductive and developmental toxicology studies have not yet been conducted with lorigerlimab consistently with the expectations for this early phase of clinical development in accordance with ICH S6(R1) (2011) and ICH M3(R2) (2009). * Known hypersensitivity to recombinant proteins, polysorbate 80, or any excipient contained in the Lorigerlimab drug formulation.