A Study to Evaluate Long-term Safety in Participants Who Have Participated in Other Luspatercept (ACE-536) Clinical Trials

A Phase 3b, open-label, single-arm, rollover study to evaluate the long-term safety of luspatercept, to the following participants: * Participants receiving luspatercept on a parent protocol at the time of their transition to the rollover study, who tolerate the protocol-prescribed regimen in the parent trial and, in the opinion of the investigator, may derive clinical benefit from continuing treatment with luspatercept * Participants in the follow-up phase previously treated with luspatercept or placebo in the parent protocol will continue into long-term post-treatment follow-up in the rollover study until the follow-up commitments are met * The study design is divided into the Transition Phase, Treatment Phase and Follow-up Phase. Participants will enter transition phase and depending on their background will enter either the treatment phase or the Long-term Post-treatment Follow-up (LTPTFU) phase * Transition Phase is defined as one Enrollment visit * Treatment Phase: For participants in luspatercept treatment the dose and schedule of luspatercept in this study will be the same as the last dose and schedule in the parent luspatercept study. This does not apply to participants that are in long-term follow-up from the parent protocol * Follow-up Phase includes: \- 42 Day Safety Follow-up Visit * During the Safety Follow up, the participants will be followed for 42 days after the last dose of luspatercept, for the assessment of safety-related parameters and adverse event (AE) reporting \- Long-term Post-treatment Follow-up (LTPTFU) Phase * Participants will be followed for overall survival every 6 months for at least 5 years from first dose of luspatercept in the parent protocol, or 3 years of post-treatment from last dose, whichever occurs later, or until death, withdrawal of consent, study termination, or until a subject is lost to follow-up. Participants will also be monitored for progression to AML or any malignancies/pre-malignancies. New anticancer or disease related therapies should be collected at the same time schedule Participants transitioning from a parent luspatercept study in post-treatment follow-up (safety or LTPTFU) will continue from the same equivalent point in this rollover study. The ACE-536-LTFU-001 rollover study will be terminated, and relevant participants will discontinue from the study when all participants fulfill 5 years on the study, including treatment and follow-up.

Inclusion Criteria: Participants must meet all the following criteria to be enrolled in this study: 1. Participant is ≥ 18 years at the time of signing the informed consent form (ICF). 2. Participant is willing and able to adhere to the study visit schedule and other protocol requirements. 3. Participant has been participating in a luspatercept trial and continues to fulfill all the requirements of the parent protocol and the participant has been either: 1. Assigned to luspatercept treatment, continues to receive clinical benefit in the opinion of the investigator and should continue to receive luspatercept treatment, OR 2. Assigned to placebo arm in the parent protocol (at the time of unblinding or in follow-up) and should cross over to luspatercept treatment, OR 3. Assigned to the Follow-up Phase of the parent protocol, previously treated with luspatercept or placebo in the parent protocol who shall continue into LTPTFU phase in the rollover study until the follow-up commitments are met (unless requirements are met as per parent protocol to crossover to luspatercept treatment). 4. Participant understands and voluntarily signs an informed consent document prior to any study-related assessments or procedures being conducted. 5. Participant demonstrates compliance, as assessed by the investigator, with the parent study protocol requirements. 6. Applies to on treatment Participants only- females of childbearing potential (FCBP) defined as a sexually mature woman who: 1\) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy, or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy or amenorrhea due to other medical reasons does not rule out childbearing potential) for at least 24 consecutive months (ie, has had menses at any time in the preceding 24 consecutive months) must: 1. Have two negative pregnancy tests as verified by the investigator prior to starting study therapy. She must agree to ongoing pregnancy testing during the course of the study, and after end of study therapy. This applies even if the participant practices true abstinence from heterosexual contact. 2. Agrees to use, and be able to comply with highly effective, contraception without interruption, 35 days prior to starting investigational product (IP), during the study therapy (including dose interruptions), and for 84 days after discontinuation of study therapy. 7\. Applies to on treatment participants only- Male participants must: a. Agrees to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study, during dose interruptions and for at least 84 days following investigational product discontinuation even if he has undergone a successful vasectomy. Exclusion Criteria: The presence of any of the following will exclude a participant from enrollment: 1. Applies to on treatment participants only- Concomitant use of any medications/procedures that are prohibited in the parent luspatercept protocol. 2. Participant has met one or more criteria for study discontinuation as stipulated in the parent luspatercept protocol. 3. Applies to on treatment participants only- More than 26 days between last luspatercept dose in the parent protocol and first dose into ACE-536-LTFU-001 protocol unless dose delay or dose discontinuation criteria met. 4. Applies to on treatment participants only- Pregnant or breastfeeding females. 5. Participant has any significant medical condition, laboratory abnormality, psychiatric illness, or is considered vulnerable by local regulations (eg, imprisoned or institutionalized) that would prevent the subject from participating in the study. 6. Participant has any condition including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study. 7. Participant has any condition that confounds the ability to interpret data from the study.