This is a randomized, double-blind, placebo-controlled, Phase 2/3 study comparing the efficacy and safety of elenestinib (BLU-263) + symptom directed therapy (SDT) with placebo + SDT in participants with indolent systemic mastocytosis (ISM) whose symptoms are not adequately controlled by SDT. Parts 1 and 2 will enroll participants with ISM. Participants enrolled in Part 2 will roll over onto Part 3 to receive treatment with elenestinib in an open-label fashion following completion of the earlier Part. Part K will enroll participants with ISM who have previously received an approved selective KIT inhibitor. The study also includes pharmacokinetic (PK) groups that will enroll participants with ISM.

Key Inclusion Criteria:

All Participants:

-Participant must have an Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 to 2.

Part 1 and PK groups:

• Participant has confirmed diagnosis of ISM, confirmed by Central Pathology Review
• Participant must have failed to achieve adequate symptom control for 1 or more Baseline symptoms, as determined by the Investigator, with at least 2 of the following symptom-directed therapies administered: H1 blockers, H2 blockers, proton-pump inhibitors, leukotriene inhibitors, cromolyn sodium, corticosteroids, or omalizumab.
• Participants must have SDT for ISM symptom management stabilized for at least 14 days prior to starting screening procedures.
• For participants receiving corticosteroids, the dose must be ≤ 20 mg/day prednisone or equivalent, and the dose must be stable for ≥ 14 days.

Part K:

-Participant has confirmed diagnosis of ISM, confirmed by Central Pathology Review

Part S:

-Participant has confirmed diagnosis of SSM, confirmed by Central Pathology Review of BM biopsy and central review of B- and C-findings by WHO diagnostic criteria.

Part 2:

-Participant has confirmed diagnosis of ISM, confirmed by Central Pathology Review

Key Exclusion Criteria:

• Participant has been diagnosed with any of the following WHO systemic mastocytosis (SM) sub-classifications: cutaneous mastocytosis only, SM with an associated hematologic neoplasm of non-MC lineage (SM-AHN), aggressive SM, mast cell leukemia, or mast cell sarcoma.
• Participant has been diagnosed with another myeloproliferative disorder.
• Participant has organ damage attributable to SM.
• Participant has clinically significant, uncontrolled, cardiovascular disease
• Participant has a QT interval corrected using Fridericia's formula (QTcF) > > 470 milliseconds (msec) (for females) or > 450 msec (for males).
• Participant has a history of a primary malignancy that has been diagnosed or required therapy within 3 years. The following prior malignancies are not exclusionary: completely resected basal cell and squamous cell skin cancer, curatively treated localized prostate cancer, and completely resected carcinoma in situ of any site.
• Time since any cytoreductive therapy including masitinib and midostaurin should be at least 5 half-lives or 14 days (whichever is longer), and for cladribine, interferon alpha, pegylated interferon, or antibody therapy < 28 days or 5 half-lives of the drug (whichever is longer), before beginning the screening period.
• Participant has received radiotherapy or psoralen and ultraviolet A (PUVA) therapy < 14 days before beginning the screening period.

Other protocol-defined criteria apply.