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:

               1. Cytochrome P450 3A4 isozyme strong inhibitor: 5 elimination half-lives

               2. CYP3A strong or moderate inducers: 4 weeks

               3. Systemic anticancer therapy or investigational therapy 3 weeks or 5 half-lives,

               4. Immunotherapy with checkpoint inhibitor: 4 weeks

          -  Curative-intent radiation therapy ≤ 4 weeks or palliative radiation therapy,

          -  Uncontrolled or significant cardiovascular disease:

               1. QTcF at rest, where the mean QTcF interval is > 480 milliseconds

               2. Myocardial infarction within 6 months

               3. Uncontrolled angina pectoris within 6 months

               4. New York Heart Association Class 3 or 4 congestive heart failure

               5. Uncontrolled hypertension