The researchers are doing this study to find out whether adding gefitinib, trametinib, disulfiram, and sunitinib to standard chemotherapy is a more effective treatment approach for people with osteosarcoma than standard chemotherapy on its own. The researchers will also look at the safety of adding these drugs to standard chemotherapy. The researchers will also use the additional research biopsies from Cohort 1 participants to learn more about how osteosarcoma survives during chemotherapy.

Inclusion Criteria:

Cohort 1 only: Newly Diagnosed, Metastatic Osteosarcoma

1. For study entry, the suspected diagnosis of osteosarcoma may be based on clinical judgement. Biopsy confirmation is required for treatment but as this protocol has biologic aims from serial tumor samples, some patients will be enrolled prior to open biopsy. Patients must have a histologic new diagnosis of metastatic high-risk osteosarcoma to start OstEvo systemic therapy. For purposes of this protocol, newly diagnosed, high-risk metastatic osteosarcoma includes:

   1. Having at least 1 extrapulmonary metastasis, radiographic confirmation of metastasis is adequate, and/or
   2. Unresectable metastases at diagnosis as determined by the investigator

2. Patients may have started systemic conventional chemotherapy but must enroll on this study prior to day 29 of chemotherapy initiation. Having received a single standard MAP cycle (AP x 1 and HDMTX up to 2 times) of chemotherapy prior to enrollment is acceptable

Cohort 2 only: Relapsed, Metastatic Osteosarcoma

1. Patients must have achieved a radiographically confirmed complete response as determined by the investigator from initial therapy and then relapsed with metastatic high-risk osteosarcoma. No strict size criteria of pulmonary or additional nodules for eligibility are required. For purposes of this protocol, relapsed, metastatic, high-risk osteosarcoma includes:

a. First relapse within 24 months of start of first chemotherapy or b. First relapse involving more than one lung nodule, or the lung and any extrapulmonary sites or c. First relapse with pleural disruption at relapse as determined by the investigator which can be determined by CT scan and/or d. Multiply relapsed patients are eligible provided the current relapse is in the context of a radiographically confirmed complete response on the scans preceding the relapse making them potentially eligible for OstEvo 2. Patients may have received only a single cycle of ifosfamide-containing conventional chemotherapy ever and included for the relapse making them eligible for OstEvo, but must enroll on this study prior to day 22 of the first cycle post-relapse

Cohort 3 only

1. Patients with newly diagnosed osteosarcoma who are not eligible for Cohorts 1 or 2.
2. Diagnostic biopsy has insufficient material for research.
3. Must be enrolled on MSK IRB 12-245, biospecimen research protocol, with oncologic surgeries planned to be performed at MSK.
4. Orthopedic surgeon assessment is that a research biopsy will not increase the risk of local recurrence.
5. Patients must be willing to assent, and consenting party must consent to the single research biopsy prior to the initiation of chemotherapy. Patients over 18 must consent to research biopsies at study entry.

Cohorts 1 and 2 only

1. Age: Patient must be > 6 and < 50 years of age at the time of study enrollment.

2. Disease Status: Metastatic high-risk osteosarcoma with cohort specific criteria above

3. Performance Level: Karnofsky ≥ 50% for patients > 16 years of age and Lansky > 50 for patients < 16 years of age within 28 days prior to enrollment.

4. Oral Medications: Patients must be able to swallow oral medications as whole tablets/capsule form if a commercially available oral suspension is not available or if tablet dissolution is not stated in the protocol.

5. Organ Function Requirements:

   1. Adequate Hematologic function, defined as:

   i. Absolute neutrophil count > 250 cells/mcL ii. Platelet count > 50,000/mcL b. Adequate Renal Function, defined as: i. May use creatinine clearance (estimated or by cystatin C) or radioisotope GFR > 70 mL/min/1.73m2 or estimated GFR (eGFR) in pediatric patients ii. A serum creatinine based on age/sex (use the Schwartz formula for estimating GFR) c. Adequate Liver Function, defined as: i. Total bilirubin < 1.5 x ULN for age ii. AST and ALT < 3 x ULN for age d. Adequate Cardiac Function, defined as: i. No history of congenital prolonged QTc syndrome ii. Correct QT (using Fridericia's correction [QTcF]) interval < 480 msec.

1. QTcF = QT / RR(0.33), where RR = 60 / heart rate in bpm iii. Left ventricular ejection fraction (LVEF) > 55 % on echocardiogram or MUGA 6. Assent and Consent: Patients at least 7 years old and less than 18 years old must be willing to assent, and consenting party must consent to research biopsies in Cohort 1. Patients 18 years and older must consent to research biopsies at study entry. All patients and/or their parents or legal guardians must have the ability to understand and the willingness to sign a written informed consent or assent document.

7. Tumor Tissue: Patients must have adequate biopsy tumor tissue, or the patient is willing to undergo a pretreatment research biopsy. A research biopsy following cycles 1 and 2 of treatment done with the thoracotomy procedure will be required. Availability of these paired biopsies will be informative to understanding mechanisms of response and resistance to initial therapy in osteosarcoma and may benefit future patients with this rare cancer.

8. Concurrent Study Enrollment: Must be enrolled on MSK IRB 12-245, biospecimen research protocol, with oncologic surgeries planned to be performed at MSK.

9. Pregnancy or Breast Feeding: The effects of the chemotherapeutic agents in OstEvo on the developing human fetus are unknown. For this reason and because OstEvo agents as well as other therapeutic agents used in this trial are known to be teratogenic, participants of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) during study therapy and for 12 months following the completion of study therapy. Should a participant become pregnant or suspect pregnancy while participating in this study, they should inform their treating physician immediately.

10. Contraception: Women of childbearing potential should adhere to contraception from enrollment through 12 months after completion of systemic chemotherapy administration. Men who are sexually active with women of childbearing potential should adhere to contraception from enrollment through 12 months after completion- of systemic chemotherapy administration 11. Protocol Adherence: Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and evaluations.

Exclusion Criteria:

Cohorts 1 and 2 only:

1. Patients who are receiving any other investigational agents for osteosarcoma therapy are ineligible.
2. Patient with an uncontrolled chronic or active infection or another condition where any component of OstEvo therapy would be contraindicated.
3. Patients with a history of heart disease including, but not limited to: uncontrolled hypertension within 12 months prior to enrollment; ongoing cardiac dysrhythmias ≥ grade 2 or atrial fibrillation of any grade; unstable angina, symptomatic congestive heart failure, or prior myocardial infarction.
4. Patients must not be receiving any additional medicines being given for the specific purpose of treating cancer. Alternative medications including, but not limited to cannabis-based products would not be a reason for exclusion.
5. Patients with any medical or surgical conditions that would interfere with gastrointestinal absorption of oral agents.
6. Patients may not have received prior cardiac irradiation.

Cohort 2 only:

5. Patients must not have previously been enrolled in OstEvo

Memorial Sloan Kettering Cancer Center supports the international committee of medical journal editors (ICMJE) and the ethical obligation of responsible sharing of data from clinical trials. The protocol summary, a statistical summary, and informed consent form will be made available on clinicaltrials.gov when required as a condition of Federal awards, other agreements supporting the research and/or as otherwise required. Requests for deidentified individual participant data can be made beginning 12 months after publication and for up to 36 months post publication. Deidentified individual participant data reported in the manuscript will be shared under the terms of a Data Use Agreement and may only be used for approved proposals. Requests may be made to: crdatashare@mskcc.org.