Inclusion Criteria

        Patients must be > 12 months and < 30 years at the time of enrollment on study.

        Phase I

          -  Patients with refractory or recurrent non-central nervous system (CNS) solid tumors
             not amenable to curative treatment are eligible. Patients must have had histologic
             verification of malignancy at original diagnosis or at the time of relapse. Patients
             eligible for the expansion cohort, A2, will include non-ES patients with refractory or
             recurrent non-CNS solid tumors with a deleterious alteration in germline or somatic
             genes involved in HR repair and DSBs signaling, germline or somatic assessed by prior
             comprehensive sequencing performed in a CLIA-approved (or equivalent) facility.

        Phase II

          -  Patients with refractory or recurrent Ewing sarcoma (during or after completion of
             first-line therapy). Refractory disease is defined as progression during first line
             treatment or within 12 weeks of completion of first line treatment. Recurrent disease
             includes patients who received first line treatment and experienced disease
             progression at any time point >12 weeks from the completion of first line therapy.

          -  Patients must have a histologic diagnosis of Ewing sarcoma with EWSR1- FLI1
             translocation or other EWS rearrangement at the time of initial diagnosis. Repeat
             biopsy at the time of disease recurrence is strongly encouraged but it is not
             required/mandated for enrollment.

        Disease status

          -  Patients must have either measurable or evaluable disease (see Section 7.0 for
             definitions). Measurable disease includes soft tissue disease evaluable by
             cross-sectional imaging (RECIST). Patients with bone disease without a measurable soft
             tissue component or bone marrow disease only are eligible for the phase 1 and phase 2
             study but will not be included in the OR endpoint.

          -  Performance level: Karnofsky > 50% for patients > 16 years of age and Lansky > 50% for
             patients < 16 years of age. Patients who are unable to walk because of paralysis, but
             who are up in a wheelchair, will be considered ambulatory for the purpose of assessing
             the performance score.

        Prior therapy

        Phase I Patients who have received prior therapy with an irinotecan-based or
        temozolomide-based regimen are eligible. Patients who have received prior therapy with a
        PARP inhibitor other than talazoparib are eligible.

        Phase II

          -  Patients should have received first line therapy and developed either refractory or
             recurrent disease (first relapse).

          -  Organ function: Must have adequate organ and bone marrow function as defined by the
             following parameters:

          -  Patients with solid tumors not metastatic to bone marrow:

          -  Peripheral absolute neutrophil count (ANC) >1,000/mm3 (1x109/L)

          -  Platelet count > 75,000/mm3 (75x109/L) (no transfusion within 7 days of enrollment)

          -  Hemoglobin > 9 g/dL (with or without support)

        In the phase I study, patients with solid tumors metastatic to bone marrow or with bone
        marrow hypocellularity defined as <30% cellularity in at least one bone marrow site will be
        eligible for study, but they will not be evaluable for hematologic toxicity. These patients
        must not be refractory to red cell or platelet transfusions. At least 2 of every cohort of
        3 patients (in the phase I study) must be evaluable for hematologic toxicity. If dose
        limiting hematologic toxicity is observed at any dose level, all subsequent patients
        enrolled at that dose level must be evaluable for hematologic toxicity.

          -  Adequate renal function defined as: Creatinine clearance or radioisotope GFR >
             60ml/min/1.73m2 or a serum creatinine maximum based on age/sex: age 6months to <1
             year, creatinine 0.4; 1 to < 2 years, creatinine 0.6; 2 < 6 years, creatinine 0.8; 6 <
             10 years, creatinine 1; 10 to <13 years, creatinine 1.2; 13 to < 16 years creatinine
             1.5 (males) or 1.4 (females); > 16 years, creatinine 1.7 (males) 1.4 (females)

          -  Adequate liver function defined as: normal liver function as defined by SGPT (ALT)
             concentration <5x the institutional ULN, a total bilirubin concentration <2x the
             institutional ULN for age, and serum albumin > 2g/dL.

          -  Adequate pulmonary function defined as no evidence of dyspnea at rest and a pulse
             oximetry > 94% if there is a clinical indication for determination. Pulmonary function
             tests are not required.

          -  Patients must have fully recovered from the acute toxic effects of chemotherapy,
             immunotherapy, surgery, or radiotherapy prior to entering this study:

          -  Myelosuppressive chemotherapy: Patient has not received myelosuppressive chemotherapy
             within 3 weeks of enrollment onto this study (8 weeks if received prior myeloablative
             therapy).

          -  Hematopoietic growth factors: At least 7 days must have elapsed since the completion
             of therapy with a growth factor. At least 14 days must have elapsed after receiving
             pegfilgrastim.

          -  Biologic (anti-neoplastic agent): At least 7 days must have elapsed since completion
             of therapy with a biologic agent. For agents that have known adverse events occurring
             beyond 7 days after administration, this period prior to enrollment must be extended
             beyond the time during which adverse events are known to occur.

          -  Monoclonal antibodies: At least 3 half-lives must have elapsed since prior therapy
             that included a monoclonal antibody or 28 days have elapsed since last dose of the
             monoclonal antibody with complete resolution of symptoms related to treatment.

          -  Radiotherapy: At least 2 weeks must have elapsed since any irradiation; at least 6
             weeks must have elapsed since craniospinal RT, 131I-mIBG therapy or substantial bone
             marrow irradiation (e.g., >50% pelvis irradiation).

          -  Female participant who is post-menarchal must have a negative urine or serum pregnancy
             test and must be willing to have additional serum and urine pregnancy tests during the
             study.

          -  Female or male participant of reproductive potential must agree to use effective
             contraceptive methods at screening and throughout duration of study treatment.

        Exclusion Criteria

        Pregnant or breastfeeding

          -  Pregnant or breast-feeding women will not be entered on this study. Pregnancy tests
             must be obtained in girls who are post-menarchal. Males or females of reproductive
             potential may not participate unless they have agreed to use two methods of birth
             control: a medically accepted barrier of contraceptive method (e.g., male or female
             condom) and a second method of birth control during protocol therapy. Two highly
             effective methods of contraception are required for female patients during treatment
             and for at least 7 months after completing therapy. Male patients with female partners
             of reproductive potential and/or pregnant partners are advised to use two highly
             effective methods of contraception during treatment and for at least 4 months after
             the final dose.

          -  Male and female participants must agree not to donate sperm or eggs, respectively,
             after the first dose of study drug through 105 days and 45 days after the last dose of
             study drug. Females considered not of childbearing potential include those who are
             surgically sterile (bilateral salpingectomy, bilateral oophorectomy, or hysterectomy).