Inclusion Criteria:  Histologically confirmed DD liposarcoma, with or without a WD component (WD/DD liposarcoma). Note: Patient must be willing to provide an archival tumor tissue sample that is ≤ 3 years old and of adequate quality or willing to provide a fresh pretreatment biopsy sample Advanced unresectable (i.e., where resection is deemed to cause unacceptable morbidity or mortality) and/or metastatic WD/DD liposarcoma Measurable tumor lesion(s) in accordance with RECIST version 1.1 Received 1 or more systemic cancer therapy regimens, including at least 1 anthracycline-based regimen, and had radiographic progressive disease (per RECIST version 1.1) within 6 months before the Screening Visit Resolution of any clinically relevant toxic effects of prior chemotherapy, surgery, radiotherapy, or hormonal therapy ECOG performance status of 0 or 1  Adequate bone marrow function:  Platelet count ≥ 100 × 10^9/L Hemoglobin ≥ 9.0 g/dL Absolute neutrophil count ≥ 1.5 × 10^9/L  Adequate hepatic function:  Alanine aminotransferase and aspartate aminotransferase ≤ 3 × upper limit of normal (ULN) if no liver metastases are present; ≤ 5 × ULN if liver metastases are present Total bilirubin ≤ 1.5 × ULN, or ≤ 3 x ULN in the setting of Gilbert's disease  Exclusion Criteria:  Prior treatment with any mouse double minute 2 (MDM2) inhibitor or trabectedin Other primary malignancies that have required systemic antineoplastic treatment within the previous 2 years, except for localized cancers that have apparently been cured Gastrointestinal conditions that could affect the absorption of milademetan, in the opinion of the Investigator Uncontrolled infection within the last 7 days requiring IV antibiotics, antivirals, or antifungals Known HIV infection or active Hepatitis B or C Untreated brain metastases. Note: Patients who require steroids for brain metastases must be on a stable or tapering dose of corticosteroids for at least 2 weeks before randomization. If applicable, patients must complete stereotactic radiosurgery 7 days before and whole brain radiotherapy 21 days before their first dose of study drug.  Investigational therapy administered within the 28 days or 5 half lives:  Cytochrome P450 3A4 isozyme strong inhibitor: 5 elimination half-lives CYP3A strong or moderate inducers: 4 weeks Systemic anticancer therapy or investigational therapy 3 weeks or 5 half-lives, Immunotherapy with checkpoint inhibitor: 4 weeks Curative-intent radiation therapy ≤ 4 weeks or palliative radiation therapy,  Uncontrolled or significant cardiovascular disease:  QTcF at rest, where the mean QTcF interval is > 480 milliseconds Myocardial infarction within 6 months Uncontrolled angina pectoris within 6 months New York Heart Association Class 3 or 4 congestive heart failure Uncontrolled hypertension