Inclusion Criteria:

          -  Diagnosis -- Stratum 1: Recurrent or refractory primary malignant CNS tumor patients
             Patients with a histologically confirmed diagnosis of a primary malignant
             non-brainstem CNS tumor (excluding DIPG patients) that is recurrent, progressive, or
             refractory. All tumors must have histologic verification at either the time of
             diagnosis or recurrence except patients with marker (+) CNS germ cell tumors.

        Stratum 2: Newly diagnosed DIPG patients (on-hold until pediatric RP2D has been established
        in Stratum 1) Patients with diffuse intrinsic pontine gliomas (DIPGs) will be eligible 6 to
        14 weeks post-completion of radiation therapy if they do not have any evidence of
        progression. Patients with newly diagnosed DIPGs, defined as tumors with a pontine
        epicenter and diffuse involvement of 2/3 or more of the pons, are eligible without
        histologic confirmation. Patients with pontine tumors that do not meet these criteria or
        not considered to be typical intrinsic pontine gliomas will only be eligible if the tumors
        have been biopsied and (1) are proven to be an anaplastic astrocytoma, glioblastoma
        multiforme, gliosarcoma, anaplastic mixed glioma or fibrillary astrocytoma or (2) have a
        histone mutation typically seen in DIPG. Patients with disseminated disease are not
        eligible, and MRI of spine must be performed if disseminated disease is suspected by the
        treating physician.

          -  Available Pre-trial Tumor Tissue -- Stratum 1: Recurrent or refractory primary
             malignant CNS tumor patients must have adequate pre-trial frozen or FFPE tumor
             material (minimum of 10 unstained slides) available for use in the tumor mutation
             burden studies (section 9.1.5).

        Stratum 2: Patients with DIPG who have pre-trial tumor tissue available are requested to
        submit tissue; however, this is not required for eligibility.

          -  Age -- Patient must be ≥ 1 and ≤ 21 years of age at the time of enrollment.

          -  Prior Therapy -- Newly Diagnosed DIPG patients Patients must have not received any
             prior therapy for treatment of their current CNS malignancy other than radiation
             therapy.

        Refractory/Recurrent patients Patients must have recovered from the acute treatment related
        toxicities (defined as < grade 1) of all prior chemotherapy, immunotherapy, radiotherapy or
        any other treatment modality prior to entering this study.

        Myelosuppressive chemotherapy -- Patients must have received their last dose of known
        myelosuppressive anticancer therapy at least 21 days prior to enrollment or at least 42
        days if nitrosourea.

        Biological agent: Patient must have recovered from any acute toxicity potentially related
        to the agent and received their last dose of the biologic agent ≥ 7 days prior to study
        enrollment.

        For agents that have known adverse events occurring beyond 7 days after administration,
        this period must be extended beyond the time during which adverse events are known to
        occur.

        Monoclonal antibody treatment and agents with known prolonged half-lives: At least three
        half-lives must have elapsed prior to enrollment.

        Radiation --

        Patients must have had their last fraction of:

        Craniospinal irradiation (>24Gy) or total body irradiation or radiation to greater than 50%
        of pelvis > 3 months prior to enrollment.

        Focal irradiation >6 weeks prior to enrollment Local palliative irradiation (small port) ≥4
        weeks

        Autologous Stem Cell Transplant -- Patient must be ≥ 6 months since autologous bone
        marrow/stem cell transplant prior to enrollment and have CD4 counts above 200/mm3.

        Surgery -- Patients must be at least 4 weeks (28 days) from major surgery and fully
        recovered from all acute effects of prior surgical intervention.

          -  Inclusion of Women and Minorities -- Both males and females of all races and ethnic
             groups are eligible for this study

          -  Neurologic Status -- Patients with neurological deficits should have deficits that are
             stable for a minimum of 1 week prior to enrollment.

        Patients with seizure disorders may be enrolled if seizures are well controlled.

        • Performance Status -- Karnofsky Performance Scale (KPS for > 16 years of age) or Lansky
        Performance Score (LPS for ≤ 16 years of age) assessed within two weeks of enrollment must
        be ≥ 60. Patients who are unable to walk because of neurologic deficits, but who are up in
        a wheelchair, will be considered ambulatory for the purpose of assessing the performance
        score.

        • Organ Function --

        Patients must have adequate organ and bone marrow function as defined below:

        Absolute Neutrophil Count (ANC) ≥ 1.0 x 109 cells/ L Platelets ≥ 100 x 109 cells/L
        (unsupported, defined as no platelet transfusion within 7 days) Hemoglobin ≥ 8 g/dL (may
        receive transfusions) Total bilirubin ≤1.5 times institutional upper limit of normal (ULN)
        AST(SGOT)/ALT(SGPT) ≤ 3 x institutional upper limit of normal (ULN) Albumin ≥ 3 g/dl Serum
        creatinine based on age/gender as noted below. Patients that do not meet the criteria below
        but have a 24 hour Creatinine Clearance or GFR (radioisotope or iothalamate) ≥ 70
        mL/min/1.73 m2 are eligible.

        Age Maximum Serum Creatinine (mg/dL) 1 to < 2 years 0.6, 0.6 (M, F); 2 to < 6 years 0.8,
        0.8 (M, F); 6 to < 10 years 1, 1 (M, F); 10 to < 13 years 1.2, 1.2 (M, F); 13 to < 16 years
        1.5, 1.4 (M, F); ≥ 16 years 1.7, 1.4 (M, F).

        • Cardiac Function: Left Ventricular Ejection Fraction (LVEF) > 50% ECG QTc ≤ 450 msec

        • Pulmonary Function: Oxygen saturation as measured by pulse oximetry is > 93% on room air
        and no evidence of dyspnea at rest

        • Growth Factors -- Patients must be off all colony- forming growth factor(s) for at least
        1 week prior to enrollment (i.e., filgrastim, sargramostim or erythropoietin). 2 weeks must
        have elapsed if patients received PEG formulations.

          -  Pregnancy Status -- Female patients of childbearing potential must have a negative
             serum or urine pregnancy test.

          -  Pregnancy Prevention -- Female subjects with childbearing potential and male subjects
             should use effective contraception methods (or abstain from sexual activity) while
             being treated with APX005M and for 30 days following treatment.

          -  Informed Consent -- The patient or parent/guardian is able to understand the consent
             and is willing to sign a written informed consent document according to institutional
             guidelines.

        Exclusion Criteria:

        • Concurrent Illness -- Patients with any clinically significant unrelated systemic illness
        (serious infections Grade ≥ 2 or significant cardiac, pulmonary, hepatic or other organ
        dysfunction), that in the opinion of the investigator would compromise the patient's
        ability to tolerate protocol therapy, put them at additional risk for toxicity or would
        interfere with the study procedures or results.

        Patients with a history of any other malignancy, except patients with a secondary brain
        tumor if the patient's first malignancy has been in remission for at least 5 years from the
        end of treatment.

        • Concurrent Therapy -- Patients who are receiving any other anticancer or investigational
        drug therapy.

        Patients requiring systemic treatment with either corticosteroids (greater than physiologic
        replacement, defined as dexamethasone 0.75 mg/m2/day) or other immunosuppressive
        medications within 14 days of study drug administration will be excluded. However, patients
        who require intermittent use of bronchodilators or local steroid injections will not be
        excluded from the study. Please see section 5.3 for a list of acceptable and unacceptable
        concomitant medications as well as reporting requirements.

        • Presence of Bulky Tumor --

        Patients with bulky tumor on imaging are ineligible. Bulky tumor is defined as:

        Tumor with any evidence of uncal herniation or midline shift Tumor that in the opinion of
        the site investigator, shows significant mass effect

          -  Allergy -- Patients with a history of severe (Grade ≥ 3) hypersensitivity reaction to
             a monoclonal antibody are ineligible.

          -  Allogeneic Hematopoietic Stem Cell Transplantation -- Patients who have received
             allogeneic hematopoietic stem cell transplantation are ineligible.

          -  Autoimmune Diseases -- Patients with active autoimmune disease or documented history
             of autoimmune disease/syndrome that requires ongoing systemic steroids or systemic
             immunosuppressive agents, except Patients with vitiligo or well controlled
             asthma/atopy Patients with hypothyroidism stable on hormone replacement or Sjogren's
             syndrome

          -  Inability to Participate -- Patients who in the opinion of the investigator are
             unwilling or unable to return for required follow-up visits or obtain follow-up
             studies required to assess toxicity to therapy or to adhere to drug administration
             plan, other study procedures, and study restrictions.

          -  Bleeding Disorder -- Patients with a known coagulopathy or bleeding diathesis or
             require the use of systemic anticoagulant medication are not eligible.

          -  Pregnancy Status -- Female patients must not be pregnant or breast-feeding.