ctHPVDNA Response-Adapted Chemoradiation +/- Retifanlimab Treatment in Locally-Advanced Anal Cancer

This study is for people who have anal cancer and have not yet had treatment. The regular treatment for people who have anal cancer is chemoradiation therapy (CRT). CRT is when chemotherapy and radiation therapy are given at the same time. Studies show that CRT works well to treat anal cancer and prevents many people from needing surgery which may require a colostomy bag. Doctors know that CRT is an effective way to treat anal cancer. But, they are doing studies to find out how much dose of radiation and chemotherapy should be given during the CRT. Higher doses of chemotherapy and radiation could increase the risk of side effects, but lowering the dose of chemoradiation has the risk of not being as effective to treat the cancer. One way to predict whether participants need higher or lower doses of radiation therapy is to do a blood test called ctDNA (circulating tumor DNA) to test for the presence of human papillomavirus (HPV). This test is done at certain times while participants are getting CRT. This has been shown to be a marker for the presence of anal cancer. In this study, doctors will tailor lower versus higher doses of CRT based on the tumor response that is measured by ctDNA. The purpose of this study is to see if customizing the dose of chemoradiation based on the amount of ctDNA will increase survival in participants with anal cancer and/or decrease the risk of side effects. Some participants in this study whose cancer does not respond as well to the CRT may have the opportunity to receive a drug called Retifanlimab that stimulates the body's immune system. Retifanlimab is approved by the Federal Drug Administration (FDA) for treating anal cancer that is recurrent or metastatic since there is proven benefit in these situations.

Inclusion Criteria: * Participants must have histologically proven stage T1-4N+M0 or T3-T4N0M0 anal canal or anal margin squamous cell carcinoma. This may include tumors of non-keratinizing histology such as basaloid, transitional cell or cloacogenic histology. Special considerations include the following: * Participants with excision of the primary tumor but with node positive disease or residual disease at the primary if T3-T4N0 will be eligible. * Age ≥18 years * ECOG performance status 0-2 * Creatinine clearance \>30 ml/min by Cockcroft-Gault Equation. * HIV-infected participants are eligible if they meet the following eligibility criteria: * A CD4 T-cell count \>= 200/mm3 and a viral load \< 200 copies/mm3 * No history of AIDS-related complications within past year other than history of low CD4+ T-cell count (\>200/mm3) prior to initiation of combination antiretroviral therapy. * Participant must be healthy on the basis of HIV disease with high likelihood of near normal life span were it not for the anal cancer. * Participant MUST receive appropriate care and treatment for HIV infection, including antiretroviral medications when clinically indicated, and should be under the care of a physician experienced in HIV management. Participants will be eligible regardless of antiretroviral medication provided the regimen has been stable for at least 4 weeks. * Participants must be PPD negative. Alternatively, the QuantiFERON-TB assay can be used. An individual is considered positive for M. tuberculosis infection if the IFN-γ response to TB antigens is above the test cut-off (after subtracting the background IFN-γ response in the negative control). The result must be obtained within 20 weeks prior to enrollment. PPD positive (or Quantiferon assay positive) participants are permitted if prophylaxis has been completed prior to enrollment. * Tumor size must be documented based on physical examination including digital rectal exam and/or anoscopy/proctoscopy within 4 weeks prior to enrollment. * Staging imaging studies must include a PET scan AND either a CT with contrast of the abdomen/pelvis or an MRI with contrast of the pelvis. It is preferred that participants receive contrast. For participants with an allergy who cannot receive pre-medication, or any other reason they can't receive IV contrast, it is recommended that they undergo an MRI of the pelvis. * Participant must have no history of prior chemotherapy for anal cancer. * Participant must not have had prior potentially curative surgery (i.e. abdominal-perineal resection) for carcinoma of the anus. However, participants who undergo local excision or excisional biopsy are eligible provided there was tumor involvement of the anal canal and/or anal verge prior to the resection, if the margins were positive, and/or if the stage is T2N0 based on tumor size before the procedure. This means that participants with T1N0M0 anal margin squamous cell carcinoma who underwent surgical excision with negative margins and no involvement of the anal verge and/or anal canal are not eligible. * Participant must not be receiving any other standard anti-cancer therapy or experimental agent. * Participant must not have intercurrent illness including, but not limited to, ongoing or active infection or psychiatric/social situations that, in the judgement of the investigator, would limit compliance with study requirements. * Participant must not have had significant cardiovascular disease within 6 months prior to enrollment that has not been treated/controlled in the opinion of the treating investigators including myocardial infarction, unstable angina, stroke, transient ischemic attack, symptomatic coronary artery disease, symptomatic congestive heart failure, or uncontrolled cardiac arrhythmia. * Participant must not have a history of a different malignancy unless they are deemed by the investigator to be at low risk of recurrence. * Participants who are on anti-coagulation with warfarin within 2 weeks prior to enrollment must use an alternative anti-coagulant if planned to receive Capecitabine, otherwise, they must receive infusional 5-FU. * NOTE: Low molecular weight heparin is permitted provided the participant's PT/INR is \< 1.5. Participants who will received capecitabine and are on Dilantin for a seizure disorder must have Dilantin levels checked weekly. * Participants must have normal organ and marrow function as defined below: * Hemoglobin ≥ 10.0 g/dl * Platelet count ≥ 100,000/mcL * Absolute neutrophil count ≥ 1,500/mcL * Total bilirubin must be \1.5 X ULN. Participants with a known history of Gilbert's disease are eligible without regard to bilirubin and liver function tests at the discretion of the treating physician. * AST/ALT must be \