DRUG: tucatinib
For Cohort 1A, 150 mg will be administered twice daily by mouth (orally) from Cycle 1 Day 8 onwards. For all other cohorts, 300 mg (or intermediate dose) will be given orally twice daily starting on Cycle 1 Day 1.
DRUG: trastuzumab
Cohorts 1A and 1B: a 6 mg/kg loading dose will be given into the vein (IV; intravenously) on Cycle 1 Day 1, followed by a dose of 4 mg/kg IV every 2 weeks starting on Cycle 2 Day 1. Cohorts 1C, 1D, 1E, 1F, 1G, 2A, and 2B: an 8 mg/kg loading dose will be administered IV on Cycle 1 Day 1, followed by a dose of 6 mg/kg IV every 3 weeks thereafter.
DRUG: oxaliplatin
85 mg/m\^2 given IV every 2 weeks for cohorts using FOLFOX. For cohorts using CAPOX regimen, 130 mg/m\^2 given every 3 weeks.
DRUG: leucovorin
200 (mFOLFOX7) or 400 (mFOLFOX6) mg/m\^2 given IV every 2 weeks. Part of FOLFOX regimen.
DRUG: fluorouracil
400 mg/m\^2 (IV bolus after leucovorin) and/or 2400 mg/m\^2 (continuous infusion over 46 hours). Part of FOLFOX regimen.
DRUG: capecitabine
1000 mg/m\^2 is taken twice per day orally on Days 1-14 of each 3 week cycle. Part of CAPOX regimen.
DRUG: pembrolizumab
400 mg given by IV on day 1 of cycle 1, then every 6 weeks.