Neoadjuvant Dual Checkpoint Inhibition and Cryoablation in Relapsed/Refractory Pediatric Solid Tumors

Inclusion Criteria: * Informed Consent: Guardian/parent or patient capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations. * Age: \>1 year and \<40 years at time of enrollment on study. * Diagnosis: histologically confirmed solid tumors (at time of original diagnosis or relapse), including osteosarcoma, Ewing sarcoma family of tumors, and rhabdomyosarcoma for disease-specific arms. For non-statistical cohort, other types of tumors are eligible, including but not limited to melanoma, hepatic tumors, Wilms tumor, neuroblastoma, and non-rhabdomyosarcoma soft tissue sarcomas. * Measurable/Evaluable Disease: Patients must have at least TWO measurable/evaluable solid target lesions. * Candidate for Cryoablation Therapy: Patients must have at least one tumor available for cryoablation therapy. * Therapeutic options: The patient's cancer must have relapsed after or failed to respond to frontline curative therapy and there must not be other potentially curative treatment options available. Curative therapy may include surgery, radiation therapy in past, chemotherapy, or combination of these modalities. * Performance Status: Karnofsky ≥50% for patients \>16 years of age and Lansky ≥60% for patients ≤16 years of age. Patients who are unable to walk because of paralysis but are up in a wheelchair, will be considered ambulatory for purpose of assessing performance score. * Prior Therapy: * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to enrolling on this study. * No limitation on the number of prior chemotherapy regimens that the patient may have • received prior to study entry. * Myelosuppressive chemotherapy: At least 21 days after last dose of cytotoxic or myelosuppressive chemotherapy and at least 6 weeks after last dose of nitrosurea. * Immunotherapy: At least 21 days must have elapsed from infusion of last dose of antibody, interleukins, interferons, and cytokines. Toxicity related to prior antibody therapy must be recovered to Grade ≤1. * Biologic (anti-cancer agent): The last dose must be at least 7 days prior to study entry. * Radiation/Cryoablation therapy: Patient must still be a candidate for additional radiation therapy or cryoablation therapy as deemed by study team's radiation oncologist/interventional radiologist. * Stem Cell Transplantation: * Allogeneic (non-autologous) bone marrow or stem cell transplant or any stem cell infusion including DLI or boost infusion: ≥100 days after infusion, no evidence of GVHD and no requirement for immunosuppression. * Autologous stem cell infusion including boost infusion or cellular therapy (eg. Modified T cells, NK cells, dendritic cells): ≥42 days must have elapsed since infusion prior to study entry. * Growth Factors: At least 14 days after last dose of a long-acting growth factor (such as pegfilgrastim) or 7 days for short acting growth factor. * Concurrent Therapies: No chemotherapy or biologic therapy is permitted. * Adequate normal organ and marrow function as defined below: * Absolute neutrophil count (ANC) ≥ 750 per mm3. * Platelet count ≥75,000 per mm3(transfusion independent). * Serum bilirubin ≤1.5 x institutional upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology. * AST (SGOT)/ALT (SGPT) ≤3x institutional upper limit of normal unless liver metastases are present, in which case it must be ≤5x ULN. * Age adjusted normal serum creatinine (see table below) OR a measured creatinine clearance (CL) \>70 mL/min or Calculated creatinine clearance \>70 mL/min by the Schwartz equation, by radioisotope GFR, or 24-hour urine collection. * Evidence of negative urinary or serum pregnancy test for post-menarchal females. * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. Exclusion Criteria: * Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study. * Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria. * Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable. * Major surgical procedure within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent and central line placement are acceptable. * History of allogenic organ transplantation. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Patients with celiac disease controlled by diet alone * Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent. * History of another primary malignancy except for * Malignancy treated with curative intent and with no known active disease ≥5 years before the first dose of IP and of low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease * History of leptomeningeal carcinomatosis. * Known brain metastases or spinal cord compression. Patients with suspected brain metastases at screening should have an MRI (preferred) or CT each preferably with IV contrast of the brain prior to study entry (skull/bone metastases allowed if does not invade dura and no evidence of CNS edema associated). * History of active primary immunodeficiency. * Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and if needed radiographic testing, and TB testing in line with local practice), hepatitis B (known positive HBV surface antigen (HBsAg) result), hepatitis C, or human immunodeficiency virus (positive HIV 1/2 antibodies). Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. * Current or prior use of immunosuppressive medication within 14 days before the first dose of nivolumab or ipilimumab. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) * Systemic corticosteroids at physiologic doses * Steroids as premedication for hypersensitivity reactions (e.g., as premedication for blood products or CT scan premedication) * Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 30 days after the last dose of IP. * Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 180 days after the last dose of nivolumab and ipilimumab combination therapy. * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. * Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy. * All AEs while receiving prior immunotherapy must have completely resolved or resolved to baseline prior to screening for this study. * Must not have experienced a ≥Grade 3 immune related AE or an immune related neurologic or ocular AE of any grade while receiving prior immunotherapy. NOTE: Patients with endocrine AE of ≤Grade 2 are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic. * Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not currently require maintenance doses of \> physiologic dosing of prednisone or equivalent per day. * Judgment by the investigator that the patient is unsuitable to participate in the study and the patient is unlikely to comply with study procedures, restrictions and requirements. * Known allergy or hypersensitivity to IP therapies.