Inclusion Criteria:

* Lower risk MDS patients (IPSS-R score ≤ 3.5 at diagnosis) who have progressed or are refractory to/intolerant of prior therapy and meet one of the following categories:

* RBC transfusion dependent according to IWG criteria must either be unresponsive to prior ESA therapy or have an EPO level \> 500
* Prior HMA therapy
* Patients with the following cytopenias who otherwise are felt to require treatment per the treating physician:

* Platelets \< 50k/uL
* ANC \< 500 cells/uL
* Patients with MDS with isolated del(5q) ("5q- syndrome") must have progressed on or not tolerated lenalidomide
* Patients who are not felt to be candidates for or lack other standard treatment options. Patients with prior luspatercept exposure are eligible.
* Patients with dysplastic type CMML (WBC \< 13,000 cells/uL) meeting the above criteria are eligible; responses will be assessed using MDS criteria
* Age ≥18 years. Because no dosing or adverse event data are currently available on the use of MGB453 in participants \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials.
* ECOG performance status ≤2 (see Appendix A).
* Participants must have adequate organ and marrow function as defined below within 21 days of treatment:

* Total bilirubin ≤ 2 mg/dL (unless due to Gilbert's in which case it must be \<3 mg/dL)
* AST(SGOT)/ALT(SGPT) ≤3 × institutional ULN
* Creatinine clearance ≥30 mL/min/1.73 m2 (by MDRD calculation)
* Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load over the prior 6 months are eligible for this trial.
* Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better.
* Ability to understand and the willingness to sign a written informed consent document.

Exclusion Criteria:

* Participants who have had chemotherapy or radiotherapy within 14 days or five half-lives, whichever is shorter, prior to the first dose of study treatment.
* Participants who are receiving any other investigational agents; a washout of 14 days or 5 half-lives, whichever is longer, is required. The washout period for biologic agents should be 28 days since the last dose.
* Prior exposure to a TIM-3 inhibitor.
* Active autoimmune disease requiring \> 10 mg per day of prednisone or the equivalent. Inactive or controlled autoimmune disease is allowed.
* Prior solid organ transplant is exclusionary. Patients with prior hematopoietic cell transplant are eligible if they are over 6 months from transplant and not on any related immunosuppressive therapy.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to MBG453.
* Active untreated or concurrent malignancy that is distinct in primary site or histology, excluding:

* The following will not be exclusionary: non-melanoma skin cancer, noninvasive colonic polyps, superficial bladder tumors, cervical cancer in-situ, ductal carcinoma in situ of the breast, monoclonal B-cell lymphocytosis, or monoclonal gammopathy of undetermined significance.
* Hormonal therapy is allowed.
* History of other malignancy is allowed if not requiring active management.
* Other malignancies that were treated with curative intent at least 1 year prior to study screening and without evidence of active disease will be allowed.
* Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial pending discussion with the principal investigator.
* Participants with uncontrolled intercurrent illness.
* Participants must not have clinically active HBV or HCV; testing is not required
* Receipt of a live vaccination within 28 days of cycle 1 day 1
* Participants with psychiatric illness/social situations that would limit compliance with study requirements.
* Female contraception is required. Pregnant women are excluded from this study because MBG453 is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with MBG453, breastfeeding should be discontinued. Women of child-bearing potential should use highly effective methods of contraception during treatment and for 150 days after the last dose of MBG453.