A Safety Study Adding Niraparib and Dostarlimab to Radiation Therapy for Rectal Cancers

This clinical trial is designed to determine the maximum tolerated dose of niraparib when combined with dostarlimab and hypofractionated radiation for locally advanced rectal cancer. Once this is determined, this dose will be tested to identify what impact it has on the tumor as well as patient reported outcome measures.

Standard of care therapy for resectable locally advanced rectal cancer includes pelvic radiation (short or long course), chemotherapy, and (if indicated) surgery. In this study, participants will: * Take niraparib by mouth once daily for up to 12 weeks. * Receive radiation therapy once daily for five days (Monday through Friday). * Receive intravenous (IV) dostarlimab once every three weeks for up to 12 weeks. * Provide feedback about how they feel and their quality of life. This is done through short surveys as well as discussing with the study team. * Undergo a sigmoidoscopy (i.e. scope of the tumor) and biopsy about halfway through treatment * Provide tumor tissue and blood samples for analysis