Study of ACTR T Cell Product in Combination With Trastuzumab in Subjects With HER2-Positive Advanced Solid Tumor Cancers

Inclusion Criteria: * Signed written informed consent obtained prior to study procedures * Histologically-confirmed Her2 positive advanced solid tumor malignancy with documented disease progression during or immediately following the immediate prior therapy, or within 6 months of completing adjuvant therapy for subjects with breast cancer * Subjects must have previously received adequate standard therapy for treatment of their malignancy * For those with metastatic breast cancer, must have received HER2-directed therapy including trastuzumab, pertuzumab and ado-trastuzumab in any breast cancer disease setting * For those with advanced gastric cancer, adequate prior treatment with HER2-directed chemotherapy is required * At least 1 measurable lesion by iRECIST * Able to provide fresh tumor biopsy or archived block specimen taken since time of most recent anti-HER2 mAb-directed therapy * ECOG of 0 or 1 * Life expectancy ≥ 6 months * LVEF ≥ 50% by MUGA or ECHO * Absolute neutrophil (ANC) count ≥ 1500/ µL * Platelet count ≥ 100,000/µL * Hemoglobin ≥ 9g/dL * Estimated GFR \>30mL/min/1.73m2 Exclusion Criteria: * glioblastoma multiforme or other primary CNS tumors are excluded * clinically significant cardiac disease * clinically significant active infection * clinical history, prior diagnosis, or overt evidence of autoimmune disease * current use of more than 5mg/day of prednisone (or an equivalent glucocorticoid) * Prior treatment as follows: * prior cumulative doxorubicin dose greater than or equal to 300 mg/m\^2 or equivalent * chemotherapy within 2 weeks of enrollment * external beam radiation within 2 weeks of enrollment (28 days if CNS-directed therapy) * any monoclonal antibody (mAb) or other protein therapeutic containing Fc-domains within 4 weeks of enrollment * pertuzumab within 4 months of enrollment * Experimental agents within 3 half-lives or 28 days prior to enrollment, whichever is shorter * allogeneic hematopoietic stem cell transplant (HSCT) * prior infusion of a genetically modified therapy * Pregnant or breastfeeding