Overview

The purpose of this study is to characterize safety and to determine the Recommended Phase 2 Dose (RP2D[s]) and optimal dosing schedule(s) of JNJ-88549968, in part 1 (Dose Escalation); to characterize the safety of JNJ- 88549968 at RP2D(s), in part 2 (Cohort Expansion).

Eligibility

Inclusion Criteria:

• Be greater than or equal to (>=) 18 years of age (or the legal age of majority in the jurisdiction in which the study is taking place, whichever the greater) at the time of informed consent
• Positive for a calreticulin (CALR) driver mutation of essential thrombocythemia (ET) or myelofibrosis (MF)
• Participants with ET and MF with risk characteristics as described in the protocol
• Have an Eastern Cooperative Oncology Group (ECOG) performance status grade of less than or equal to (<=) 2

Exclusion Criteria:

• Known allergies, hypersensitivity, or intolerance to the excipients of the study treatment
• Concurrent or recently diagnosed or treated malignancies present at the time of participant screening. Exceptions are squamous and basal cell carcinoma of the skin, carcinoma in situ of the cervix, and any malignancy that is considered cured or has minimal risk of recurrence within 1 year of first dose of study treatment in the opinion of both the investigator and sponsor's medical monitor. Participants cured of another malignant disease with no sign of relapse greater than or equal to (>=) 3 years after treatment ended are allowed to enter the study
• Prior solid organ transplantation
• Either of the following regarding hematopoietic stem cell transplantation:
  1. Prior treatment with allogenic stem cell transplant less than or equal to (<=) 6 months before the first dose of JNJ-88549968 or
  2. Evidence of graft versus host disease (GVHD) that requires immunosuppressant therapy
• History of clinically significant cardiovascular disease within 6 months prior to

  the first dose of study treatment