This is a Phase 2, randomized, double-blind, placebo-controlled study comparing the efficacy and safety of avapritinib + best supportive care (BSC) with placebo + BSC in patients with indolent systemic mastocytosis (ISM) whose symptoms are not adequately controlled by BSC. The study will be conducted in 3 parts. All patients will receive treatment with avapritinib during Part 3 including those rolling over from the placebo group.