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

This is a phase II, open-label, non-randomized, multi-institutional study investigating postoperative or adjuvant human epidermal growth factor receptor (HER2)-directed therapy with adjuvant ado-trastuzumab emtansine (T-DM1) in HER2-positive salivary gland carcinomas (SGC). This research study is: * Studying the use of T-DM1 in combination with radiation and chemotherapy; and the use of maintenance T-DM1 alone for up to a year after surgery * Evaluating the effectiveness, safety, and toxicity of T-DM1 T-DM1 is a specialized antibody targeting HER-2 (a protein that is expressed in some breast and salivary gland cancers). The drug is a HER-2 antibody that is bound to a chemotherapy agent (DM1) and delivered intravenously. T-DM1 then binds cancer cells that express HER-2 and is taken up into the cell to allow DM1 to kill cancer cells in a more targeted way. This allows the use of a targeted treatment along with chemoradiation to treat HER-2 expressing salivary cancers. The U.S. Food and Drug Administration (FDA) has not approved T-DM1 for HER2-positive salivary gland cancer but it has been approved for other uses (for breast cancers that express HER2 protein). The research study procedures include: screening for eligibility and study treatment including evaluations and follow up visits. This research study involves radiation, chemotherapy, and targeted therapy given after surgery for up to 1-year, and participants will be followed for 3 years. It is expected that about 55 people will take part in this research study. Genentech is supporting this research study by providing the research study drug, T-DM1.