Criteria:  Refractory or unlikely to respond (erythropoietin [EPO] >= 200 U/L) or documented intolerance to erythropoiesis stimulating agent (ESA). Patients should have either a documented intolerance or contraindication to ESA or a lack of response after ESA therapy trial of at least four weeks; and ESA therapy should be stopped four weeks prior to trial enrollment  Inclusion Criteria:  Age >= 18 years Patients with a World Health Organization(WHO)-defined diagnosis of MDS/MPN-RS-T or MDS/MPN-U with >= 15% RS Prior treatment with lenalidomide, hypomethylating agents, immunosuppressive therapy or investigational agent is allowed as long as patients have not received luspatercept-aamt or sotatercept. If there is prior history of investigational agent, there should be an interval equivalent to at least four elimination half-lives of the agent prior to enrollment. Note: For patients who have received prior lenalidomide, hypomethylating agents, or immunosuppressive therapy, there must be >= 6 weeks since the last dose before luspatercept-aamt treatment is started Eastern Cooperative Oncology Group (ECOG) performance score of 0, 1 or 2 Requirement of red blood cell transfusions (>= 2 unit =< 8-weeks prior to registration) OR symptomatic anemia with hemoglobin < 9.5 g/dL OR hematocrit < 30% (as long as there is documentation of adequate iron stores (ferritin > 50 mg/L) =< 5 weeks prior to registration). Symptomatic anemia is defined as fatigue with or without exertion, shortness of breath with or without exertion, or decrease in exercise tolerance Hemoglobin =< 9.5 g/dL (obtained =< 14 days prior to registration) Total bilirubin =< 1.5 x upper limit of normal (ULN) (obtained =< 14 days prior to registration) Alanine aminotransferase (ALT) and aspartate transaminase (AST) =< 3 x ULN (=< 5 x ULN for patients with liver involvement) (obtained =< 14 days prior to registration) Calculated creatinine clearance >= 30 ml/min using the Cockcroft-Gault (obtained =< 14 days prior to registration)  Females of childbearing potential (FCBP) defined as a sexually mature woman who:  Has achieved menarche at some point Has not undergone a hysterectomy or bilateral oophorectomy, or  Has not been naturally postmenopausal (amenorrhea following cancer therapy 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) and must:  Must have two negative urine or serum pregnancy tests as verified by the investigator prior to starting study therapy. A negative pregnancy test must be done =< 7 days prior to registration. Patient must agree to ongoing pregnancy testing during the course of the study, and after end of study therapy. This applies even if the subject practices true abstinence from heterosexual contact  Either commit to true abstinence*from heterosexual contact (which must be reviewed on a monthly basis and source documented) or agree to use, and be able to comply with highly effective, contraception without interruption during the study therapy (including dose interruptions), and for 84 days after discontinuation of study therapy  True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [eg, calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception)  Male participants must:  Practice true abstinence (which must be reviewed on a monthly basis) or agree 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  True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [eg, calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception) Provide written informed consent Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) Willingness to provide mandatory blood specimens for correlative research  Exclusion Criteria:  Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects:  Pregnant persons Nursing persons Persons of childbearing potential who are unwilling to employ highly effective contraception  Any of the following prior therapies:  Surgery =< 3 weeks prior to registration Chemotherapy or other agents =< 2 weeks prior to registration  Uncontrolled intercurrent non-cardiac illness including, but not limited to:  Ongoing or active infection Uncontrolled hypertension (defined as systolic blood pressure >= 140 mmHg or diagnostic blood pressure >= 90 mmHg despite use of >= 3 anti-hypertensive drugs at optimal doses) Psychiatric illness/social situations Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy Clinically significant (symptomatic) anemia either due to nutritional deficiencies or iron, vitamin B12, folate or gastrointestinal (GI) bleeding Any other conditions that would limit compliance with study requirements  Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy  NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state (CD4 =< 200 x 10^6/L), are eligible for this trial Receiving any other drug (except hydroxyurea) or investigational agent which would be considered as a treatment for the primary disease, that is, MDS/MPN-RS-T or MDS/MPN-U with RS =< 2 weeks prior to registration  Other active malignancy =< 3 years prior to registration. Patients on hormonal therapy for treated breast or prostate cancer are permitted if they meet other eligibility criteria  EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix. NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment (luteinizing hormone-releasing hormone (LHRH) agonists for prostate cancer, and treatment with bisphosphonates and receptor activator of nuclear factor kappa-B ligand [RANKL] inhibitors) for their cancer History of myocardial infarction, stroke, embolism, deep vein or arterial thrombosis =< 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias