Inclusion Criteria:

• Age ≥12 and ≤40 years.
• Histologically confirmed relapsed or refractory sarcoma (Phase 1) or osteosarcoma (Phase 2).
• At least one prior standard systemic therapy regimen.
• Not candidates for available therapies known to provide survival benefit.
• Karnofsky/Lansky performance score ≥60.
• Life expectancy ≥16 weeks.
• Adequate organ function: ANC ≥1,000/mcL, Platelets ≥100,000/uL, Hemoglobin ≥8 g/dL, Adequate hepatic and renal function.
• Ability to swallow tablets.
• Negative pregnancy test for females of childbearing potential.
• Agreement to use effective contraception.
• Ability to provide informed consent/assent.

Exclusion Criteria:

• Receiving another investigational agent.
• Receiving concurrent anticancer therapy.
• Known hypersensitivity to domatinostat or sirolimus.
• Bone marrow-only disease.
• CNS metastatic disease.
• Major surgery within 2 weeks prior to treatment.
• Active malignancy within the previous 3 years (with protocol-specified exceptions).
• History of solid organ transplantation.
• Significant recent cardiac disease.
• Concurrent prohibited CYP3A4/P-gp interacting medications.
• Uncontrolled infection or other serious uncontrolled illness.
• Pregnancy or breastfeeding.
• HIV infection on antiretroviral therapy.
• Weight <40 kg.
• Inability to comply with study requirements.