There will be two phase II cohorts for pembro plus trastuzumab: one cohort will be for patients with unresectable HER2 overexpressing gastric or GEJ cancers, the other cohort will be for patients with HER2 overexpressing metastatic breast cancer (MBC). The pembro plus ado-trastuzumab emtansine phase II arm will be for patients with HER2 overexpressing MBC. There will be two phase II cohorts for pembro plus cetuximab: one cohort will be for patients with HNSCC, the other cohort will be for patients with K-ras, B-raf, N-ras wildtype metastatic CRC.