Immunoglobulin light chain (AL) amyloidosis is the most common form of systemic amyloidosis. AL amyloidosis has many root causes and is characterized by the overproduction of AL that are secreted by clonal bone marrow plasma cells. This is a study to determine adverse events and change in disease activity in adult participants with AL amyloidosis treated with ABBV-383. Etentamig (ABBV-383) is an investigational drug being developed for the treatment of AL amyloidosis. This study in broken into 2 parts (dose escalation and safety expansion) with 5 arms. During dose escalation (arms 1-3) participants will receive 1 of 3 doses of ABBV-383 to determine the part 2 doses. After completion of the dose escalation portion of the study, the safety expansion (part 2) portion of the study will begin. Two arms (arm 4-5) will begin and participants will receive 1 of 2 doses as determined during the dose escalation portion (part 1). Around 76 adult participants with relapsed/refractory AL amyloidosis will be enrolled at approximately 20 sites across the world. Participants will receive Etentamig (ABBV-383) as an infusion into the vein for up to approximately 2 year study duration. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic. The effect of the treatment will be checked by medical assessments, blood tests, checking for side effects and questionnaires.