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.