Vincristine and Temozolomide in Combination With PEN-866 for Adolescents and Young Adults With Relapsed or Refractory Solid Tumors

* INCLUSION CRITERIA: * Pathology: * For phase 1, Participants must have histologically or cytologically confirmed recurrent or refractory solid tumors, excluding CNS tumors and lymphoma. * For phase 2, participants must have histologically or cytologically confirmed recurrent or refractory Ewing sarcoma (Cohort 2) or embryonal or alveolar rhabdomyosarcoma (Cohort 3). Participants with Ewing sarcoma (Cohort 2 only) should have evidence of EWS translocation by FISH or RT-PCR. NOTE: Histologic confirmation of original diagnosis or relapse is required by the Laboratory of Pathology, NCI or participating site s Pathology Department. A formalin fixed tissue block or at least 5 unstained slides (10 micron thick) of archival tumor sample must be available at the time of enrollment. Participants under 18 years old without adequate archival tissue available may opt to undergo pre-treatment biopsy if it can be performed with minimal morbidity. In the event that a participants under 18 cannot safely undergo biopsy and does not have adequate archival tissue available, enrollment will be at the discretion of the Study Chair. * Measurable disease: * For phase 1, participants must have measurable (per RECIST 1.1.) or non-measurable disease on imaging, or presence of recurrent/residual disease identified on aspirate/biopsy or due to presence of elevated tumor biomarkers. * For phase 2, participants must have measurable disease, per RECIST 1.1. * Prior therapy: * For phase 1, there are no limits to the number of prior treatment regimens * For phase 2, there are no limits to the number of prior treatment regimens. However, participants must not have received any prior therapy with an irinotecan/temozolomide combination containing regimen (participants may have received either drug alone or in combination with different agents at different periods of their course). * For all participants: Participants must have recovered from the acute side effects of their prior therapy, such that eligibility criteria are met. The following prior therapies are permitted, given the indicated time has elapsed: * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive. At least 21 days must have elapsed after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea). * Anti-cancer agents not known to be myelosuppressive (which can include biologic agent, targeted agent, tyrosine kinase inhibitor, or a metronomic non-myelosuppressive regimen): \>=7 days must have elapsed after the last dose of agent. * Antibodies including checkpoint inhibitors: \>= 21 days or 3 half-lives (whichever is shorter) must have elapsed from infusion of last dose of antibody. * Systemic corticosteroids: Participants may be on physiologic steroid replacement for adrenal insufficiency or chronic corticosteroids at a stable dose for at least 7 days. Participants undergoing a steroid wean are eligible as long as no dose re-escalation has occurred in the prior 7 days. If steroids are being used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid, unless the participant is receiving physiologic steroid replacement for adrenal insufficiency. * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g., pegfilgrastim) or 7 days for short-acting growth factor. * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days must have elapsed after the completion of dose * Stem cell infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including DLI or boost infusion: \>= 84 days must have elapsed after infusion and no evidence of GVHD. * Autologous stem cell infusion including boost infusion: \>= 42 days must have elapsed. * Cellular Therapy: \>= 42 days must have elapsed after the completion of any type of cellular therapy (e.g., modified T cells, NK cells, dendritic cells, etc.). * XRT/External Beam Irradiation including Protons: \>= 84 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial bone marrow radiation. \>= 14 days after local XRT however there is no time restriction for palliative radiation with minimal bone marrow involvement and the participant has measurable/evaluable disease outside the radiation port or the site of radiation has documented progression. * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I-MIBG): \>= 42 days must have elapsed after systemically administered radiopharmaceutical therapy. * Age \>= 12 years and \<= 39 years NOTE: Because no dosing or adverse event data are currently available on the use of PEN-866 in participants \<18 years of age, children \<12 years of age are excluded from this study but will be eligible for future pediatric trials. Since the study population of interest is relapsed or refractory sarcomas which is typically seen in adolescents and young adults, and per FDA recommendations for enrolling adolescents in disease/target-appropriate adult oncology clinical trials of investigational agents, eligibility will include participants aged 12-17 years old. * ECOG performance status \<=2, (Karnofsky \>=50% for participants \> 16 years of age and Lansky \>= 50% for participants \<= 16 years of age. NOTE: Neurologic deficits in participants with CNS metastases must have been stable for at least 7 days prior to study enrollment. Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of performance. * Willingness to have a central venous access line placed if the participant does not already have one in place. * Participants must have adequate organ and marrow function as defined below: Hematologic Function: * Peripheral absolute neutrophil count (ANC) \>= 1000/mm3 * Platelet count \>=75,000/mm\^3 * Hemoglobin \>= 8 g/dL * Participants without known metastatic bone marrow disease must meet the blood counts as listed above, without requiring transfusions (defined as not receiving platelet or red blood cell transfusions for at least 7 days prior to initiation of study therapy) or growth factor support * For participants with known metastatic bone marrow disease: * Provided they meet the blood counts as listed above, without requiring transfusions (defined as not receiving platelet or red blood cell transfusions for at least 7 days prior to initiation of study therapy) or growth factor support these participants will be eligible for the phase 1 component of the study. * For the phase 2 component, participants should meet the blood counts as listed above, but may receive transfusions of red blood cells or platelets provided they are not known to be refractory to red cell or platelet transfusions. These participants will be excluded from the phase 1 component. * For participants undergoing biopsy only, adequate coagulation defined as INR \<= 1.5 Renal Function: * Creatinine clearance or radioisotope GFR \>= 60 mL/min/1.73 m\^2 or * A serum creatinine based on age/gender as follows: Age 12 to \<13 years maximum serum creatine male 1.2 female 1.2 Age 13 to \<16 years maximum serum creatine male 1.5 female 1.4 Age \>= 16 years maximum serum creatine male 1.7 female 1.4 The Cockcroft-Gault equation should be used for calculation of creatinine clearance. Liver Function: * Bilirubin (sum of conjugated + unconjugated) \<= 1.5 upper limit of normal (ULN) for age * SGPT (ALT) \<= 135 U/L. * SGOT (AST) \<= 150 U/L. Participants with Gilbert s syndrome are excluded from the requirement of a normal bilirubin unless they are found to have the UGT1A1 28/28 genotype. Gilbert s syndrome is found in 3-10% of the general population, and is characterized by mild, chronic unconjugated hyperbilirubinemia in the absence of liver disease or overt hemolysis. NOTE: Adult values will be used for calculating hepatic toxicity and determining eligibility. Cardiac Function: * Shortening fraction of \>=27% or ejection fraction of \>= 50% by echocardiogram. * QTc interval \< 470 msec * Participants with toxicities from prior therapies must have resolution of these toxicities to \<= Grade 1, with the exception of peripheral neuropathy and alopecia which must resolve to \<=Grade 2. * Participants with treated brain metastases (CNS as primary tumor not eligible) are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression. Participants must be asymptomatic from their brain metastasis and not require corticosteroids for 4 weeks prior to start of therapy (C1D1). Participants with remote history of spinal cord compression are eligible. * Participants with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy. Participants must be asymptomatic or have disease controlled with surgery and radiation and should not require steroids within 4 weeks prior to start of therapy (C1D1). * Participants with human immunodeficiency virus (HIV)-infected participants on effective anti- retroviral therapy with no detectable viral load on any tests within the last 6 months are eligible for this trial * For participants with chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy within the last 6 months. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load within the last 6 months. * Participants ages 18 years old and older must be willing to undergo tumor biopsy before treatment and have available archival tissue (specifically, a formalin fixed tissue block or at least 5 unstained slides \[10 micron thick\]) at the time of enrollment. If biopsy is contraindicated or unable to be performed and/or there is no archival tissue available, enrollment must be approved by the Study Chair. * Participants ages 12-17 years old without available archival tissue (specifically, a formalin fixed tissue block or at least 5 unstained slides \[10 micron thick\]) at the time of enrollment may opt to undergo pre-treatment biopsy if it is clinically indicated or if it can be performed with minimal morbidity using local anesthesia. In the event that a participant 12-17 cannot undergo biopsy as described above and does not have adequate archival tissue available, enrollment will be at the discretion of the Study Chair. * Individuals of childbearing potential: negative serum Beta human chorionic gonadotropin ((Beta)hCG) pregnancy test during screening. A negative pregnancy test is also required within 8 days before first treatment; screening results may be used for treatment if they fall within the required window. * Participants of reproductive potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from the time of consent, for the duration of therapy, and for 6 months after the last dose of study therapy. * Nursing participants must be willing to discontinue nursing from study treatment initiation through 6 months after completion of chemotherapy * Ability of participant (or parent or legal guardian in case of pediatric participant) to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Participants who are receiving any other investigational agents or other anticancer agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to PEN-866 (which includes ganetespib or other HSP90 inhibitors, irinotecan, SN-38, or other agents containing irinotecan, SN-38 or its derivatives) or other agents used in study (vincristine and temozolomide). * Participants who have previously discontinued vincristine, temozolomide, or irinotecan due to severe toxicity. * Participants with a history of grade 4 vincristine-related peripheral neuropathy or constipation. * Participants who require medication with any of the inhibitors of UGT1A1, substrates of CYP1A2 or substrates of the P-gp, BCRP, OATP1B1, OATP1B3, or OCT1 transporters. Participants discontinuing these drugs must undergo a washout of 2-weeks or 5 half-lives, whichever is shorter, prior to C1D1. * Uncontrolled intercurrent illness as listed below: * Unstable angina within 6 months prior to start of treatment * Myocardial infarction within 6 months prior to start of treatment * New York Heart Association Class III - IV heart failure * Clinically important abnormalities in rhythm, conduction, or morphology of resting ECG (e.g., complete left bundle branch block, third degree heart block) * Congenital long QT syndrome * Uncontrolled hypertension despite use of antihypertensives for management of hypertension * Stroke or transient ischemic attack within 6 months prior to start of treatment * As judged by the investigator, evidence of severe or uncontrolled systemic disease, active bleeding diatheses, renal or liver transplant, or Grade \>2 active infection * Any medical, psychological, or social condition that would interfere with the participant s participation in the study. * Any other uncontrolled intercurrent systemic illness that would limit compliance with study requirements * Pregnancy * Major surgery within 28 days prior to start of therapy (C1D1) * UGT1A1 Status Participants identified with a UGT1A1 28/28 genotype will be excluded from the phase 1 component of the study. In phase 2, they may receive PEN-866 with altered dosing- see Section. Participants who are known to not be homozygous for UGT1A128/28 genotype (i.e., 1/1 or 1/28) may receive the enrolling cohort dose level of PEN-866 on C1D1 during phase 1 and the RP2D of PEN-866 during phase 2.