Post-op T-DM1 in HER-2+ Salivary Gland Carcinomas

Inclusion Criteria: * Subject must have histologically or cytologically confirmed, resectable stage II (with positive margins), III, IVA, or IVB locoregionally advanced salivary gland carcinoma (including any histologic subtype), as defined by 2017 American Joint Committee on Cancer (AJCC), 8th edition. * Willing to provide tissue from a diagnostic biopsy or at the time of cancer resection, and blood samples before, during, and after treatment. * HER2 positive disease as defined by any of the following: * Tumor HER2 expression staining intensity of 2 or 3+ by IHC (from either a preoperative biopsy or resection specimen at the time of oncologic surgery) * HER2 amplification as determined by FISH (HER2/CEP 17 ratio greater than or equal to 2.0 or HER2 mean copy number greater than or equal to 4.0) * HER2 or ERBB2 mutated on tumor genomic sequencing assay (see Section 9.1 for permitted HER2 mutations) * Age 18 years or older * ECOG performance status ≤ 1 (Karnofsky ≥ 60%, see Appendix A) * Participant must have normal organ and marrow function as defined below within 14 days prior to study registration: * leukocytes ≥ 3,000/mcL * absolute neutrophil count ≥ 1,000/mcL * hemoglobin ≥ 9.0 g/dL * platelets ≥ 100,000/mcL * total bilirubin ≤ 2.0 g/dL * AST(SGOT)/ALT(SGPT) ≤ 2.5× institutional upper limit of normal * creatinine within normal institutional limits OR * creatinine clearance ≥50 mL/min/1.73 m2 for participants with creatinine levels above institutional normal * Serum calcium (corrected for albumin value), magnesium, and potassium levels within normal limits per institutional standards. * Assessment of cardiac function either by an echocardiogram or a multi-gated acquisition (MUGA) scan prior to the therapy initiation, with a baseline left systolic ventricular ejection fraction (LVEF) ≥ 50% within 1 month prior to study registration. * Ability to understand and the willingness to sign a written informed consent document. * Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 72 hours prior to the start of T-DM1. "Women of childbearing potential (WOCBP)" is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL. * Men who are sexually active with WOCBP must agree to use any contraceptive method with a failure rate of less than 1% per year. Men who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 6 months after the last dose of investigational product. Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile as well as azoospermic men) do not require contraception. See Appendix B for further guidance on contraception. Exclusion Criteria: * Patient with AJCC 2017 8th edition stage I or stage IVC (metastatic) disease, or unresectable disease. * Subject who has had prior radiation and/or chemotherapy for head and neck cancer. * Any history of prior HER2 directed therapy. * Active or uncontrolled infection. * Pregnant or lactating women. * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer, and low risk prostate adenocarcinoma being managed with active surveillance. A history of another separate malignancy in remission without evidence of active disease in the last 2 years is permitted.