After the highest tolerable dose level of the study drug combination is found, up to 20 additional participants will be enrolled in the dose expansion group. Patients with metastatic gastrointestinal stromal tumors (GIST), melanoma, or tumors with original tumor biopsies testing positive for KIT mutations (a cancer biomarker) will be eligible to enroll and will receive the highest dose of the study drug combination that was tolerated in the dose escalation group.