The main purpose of the study is to evaluate the safety and tolerability of the combination of elranatamab and carfilzomib and dexamethasone or elranatamab and maplirpacept. There are 2 parts to this study. Part 1 will evaluate the safety and tolerability of elranatamab when given in combination with carfilzomib plus dexamethasone. Part 2 has 2 arms. The first will evaluate the safety and tolerability of elranatamab when given in combination with maplirpacept. The second will identify the optimal dose(s) of elranatamab plus maplirpacept. All study medicines are given over 4-week cycles. Everyone taking part in this study will receive elranatamab as a shot under the skin. Participants in Part 1 will also receive weekly carfilzomib as an IV infusion (given directly into a vein) and dexamethasone either by mouth (as a pill) or by IV infusion. Participants in Part 2 will receive elranatamab in combination with maplirpacept as an IV infusion (given directly into a vein) The investigators will examine the experiences of people receiving the study medicines. This will help determine if the study medicines are safe and can be used for multiple myeloma treatment. Participants will take part in this study for about 2 years after the first dose.