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