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). For U.S. sites: the purpose of this study is to characterize the safety and to determine the RP2D(s) and optimal dosing schedule(s) of JNJ-88549968 in Part 1 and part 1b (Dose Escalation), and to characterize the safety of JNJ-88549968 at the RP2D(s) in Part 2 and part 2b (Cohort Expansion), when given as monotherapy in essential thrombocythemia (ET) or myelofibrosis (MF), and with ruxolitinib or momelotinib in MF only.
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
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
Prior treatment with allogenic stem cell transplant less than or equal to (<=) 6 months before the first dose of JNJ-88549968 or