The purpose of this study is to determine safety and tolerability and to establish a preliminary recommended Phase 2 dose (RP2D) for the following combinations: pembrolizumab plus binimetinib (Cohort A), pembrolizumab plus mFOLFOX7 (oxaliplatin 85 mg/m^2; leucovorin [calcium folinate] 400 mg/m^2; fluorouracil [5-FU] 2400 mg/m^2) (Cohort B), pembrolizumab plus mFOLFOX7 and binimetinib (Cohort C), pembrolizumab plus FOLFIRI (irinotecan 180 mg/m^2; leucovorin [calcium folinate]400 mg/m^2; 5-FU 2400 mg/m^2 over 46-48 hours) (Cohort D), and pembrolizumab plus FOLFIRI and binimetinib (Cohort E).