A Study of Tucatinib and Trastuzumab in People With Rectal Cancer

Inclusion Criteria: * Willing and able to provide written informed consent for the trial. * Be ≥18 years of age on the date of signing informed consent. * ECOG performance status of 0 or 1. * Histologically confirmed rectal adenocarcinoma. * Adenocarcinoma with distal margin of 15 cm or less from the anal verge on endoscopy, staged with endorectal ultrasound (ERUS) or magnetic resonance imaging (MRI) as cT3/cT4 N0 or cT(any) cN1/2, * No evidence of distant metastases * Radiologically measurable or clinically evaluable disease per Protocol Section 13.0. * Have confirmed HER2-positive rectal adenocarcinoma, as defined by having tumor tissue tested at a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory, meeting at least one of the following criteria: 1. HER2+ overexpression (3+ immunohistochemistry \[IHC\]) by an FDA-approved HER2 IHC test following the package insert's interpretational manual for gastric cancer 2. HER2 2+ IHC is eligible if the tumor is amplified by an FDA-approved HER2 in situ hybridization assay (FISH or chromogenic in situ hybridization \[CISH\]) following the package insert's interpretational manual for gastric cancer 3. HER2 (ERBB2) amplification by CLIA-certified Next Generation Sequencing (NGS) sequencing assay. * Tumor specimen that demonstrates intact mismatch repair enzymes by immunohistochemistry or microsatellite stability as demonstrated by NGS or PCR. * Tumor specimen that indicates RAS wild-type based on expanded RAS testing including KRAS exon 2 (codons 12 and 13), exon 3 (codons 59 and 61), and exon 4 (codons 117 and 146) * Left ventricular ejection fraction \>=50 assessed by echocardiography * Negative pregnancy test done within 14 days prior to beginning treatment, for women of childbearing potential only. Subjects of childbearing potential must be willing to use an adequate method of contraception. Appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives, or double barrier method (diaphragm plus condom). Contraception is required for the course of the study starting with the first dose of study medication through 150 days after the last dose of study medication. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Nonchildbearing potential is defined as follows (by other than medical reasons): * ≥45 years of age and has not had menses for \>1 year * Patients who have been amenorrhoeic for \<2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use 2 adequate barrier methods throughout the study. * Demonstrate adequate organ function as defined in the Table 6-1 below within 14 days of Cycle 1 Day 1, all screening labs should be performed within 14 days of treatment initiation. * Absolute neutrophil count (ANC): ≥1,500 /mm3 * Platelets: ≥100,000 / mcL * Hemoglobin: \>9 g/dL or ≥5.6 mmol/L * Serum creatinine OR Measured or calculated creatinine clearance (Creatinine clearance should be calculated per institutional standard.) (GFR can also be used in place of creatinine or CrCl): ≤1.5 × upper limit of normal (ULN) OR ≥60 mL/min for subject with creatinine levels \> 1.5 × institutional ULN * Serum total bilirubin: Total bilirubin ≤ 1.5 × upper limit of normal (ULN), except for subjects with known Gilbert's disease who may enroll if the conjugated bilirubin is ≥1.5 x ULN * AST (SGOT) and ALT (SGPT): ≤ 2.5 × ULN * International Normalized Ratio (INR) or Prothrombin Time (PT) Activated Partial Thromboplastin Time (aPTT): For patients not taking warfarin: INR \<1.5 or PT \<1.5 x ULN; and either PTT or aPTT \<1.5 x ULN. Patients on warfarin may be included on a stable dose with a therapeutic INR \<3.5 Exclusion Criteria: * Recurrent rectal cancer. * Prior pelvic radiation therapy, chemotherapy, or surgery for rectal cancer. * Tumor is causing symptomatic bowel obstruction (patients who have a temporary diverting ostomy are eligible). * Other invasive malignancy ≤ 5 years prior to registration. Exceptions are non-melanoma skin cancer that has undergone potentially curative therapy and in situ cervical carcinoma. * Active infection requiring systemic therapy. * Other Anticancer or Experimental Therapy. No other experimental therapies (including chemotherapy, radiation, hormonal treatment, antibody therapy, immunotherapy, gene therapy, vaccine therapy, angiogenesis inhibitors, matrix metalloprotease inhibitors, thalidomide, anti-VEGF/Flk-1 monoclonal antibody or other experimental drugs) of any kind are permitted while the patient is receiving study treatment. * Known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies) * Known active Hepatitis B (e.g., HbsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Any known chronic (non-transient) liver disease in the patient's past medical history such as (but not limited to) cirrhosis, NASH (non-alcoholic steatohepatitis) or NAFLD. * Women who are pregnant or breastfeeding, or men expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening visit through 150 days after the last dose of study medication. * Concurrent medical or psychiatric condition or disease which, in the investigator's judgement, would make them inappropriate candidates for entry into the study. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, chronic obstructive pulmonary disease, uncontrolled major sei