This is a two-part Phase 1, non-randomized, open-label study of MM-151 plus MM-121, MM-141, or trametinib in patients with advanced, heregulin-positive lung, head and neck, and colorectal cancers. In part 1 of the study, cohorts of 3 or more patients will be treated at escalating doses of MM-151 in combination with MM-121, MM-141, and trametinib until a maximum tolerated combination dose for each combination is identified. In part 2 of the study, patients will be treated with the combination dose identified in part 1 of the study.