Inclusion Criteria:

          -  Have histologically confirmed WHO grade IV GBM or its variants. Participants will be
             eligible if the original histology was low-grade glioma and a subsequent histological
             diagnosis of GBM is made. Participants with WHO grade III recurrent malignant glioma
             will be allowed to enroll to Cohort 1 only.

          -  Be willing and able to provide written informed consent/assent for the trial.

          -  Be ≥ 18 years of age on day of signing informed consent.

          -  Have a Karnofsky performance status (KPS) ≥ 70 (Appendix A).

          -  Previous first line therapy with at least radiotherapy.

          -  Be at first or second relapse. Note: Relapse is defined as progression following
             initial therapy (i.e., radiation ± chemotherapy). For participants who had prior
             therapy for a low-grade glioma, the surgical diagnosis of a high-grade glioma will be
             considered the first relapse.

          -  Participants must have shown unequivocal evidence for tumor progression by MRI or CT
             scan.

          -  Demonstrate adequate organ function as defined in Table 1, all screening labs should
             be performed within 14 days of registration.

               -  Table 1: Adequate Organ Function Laboratory Values

                    -  System Laboratory Value

                         -  Hematological Absolute neutrophil count (ANC) ≥1,500 /mcL Platelets
                            ≥100,000 / mcL Hemoglobin ≥9 g/dL or ≥5.6 mmol/L without transfusion or
                            EPO dependency (within 7 days of assessment)

                         -  Renal Serum creatinine OR measured or calculated a creatinine clearance
                            (GFR can also be used in place of creatinine or CrCl) ≤1.5 X
                            institutional upper limit of normal (ULN) OR

                            ≥60 mL/min for participant with creatinine levels > 1.5 X institutional
                            ULN a Creatinine clearance should be calculated per institutional
                            standard.

                         -  Hepatic Serum total bilirubin ≤ 1.5 X institutional ULN OR Direct
                            bilirubin ≤ institutional ULN for participants with total bilirubin
                            levels > 1.5 institutional ULN AST (SGOT) and ALT (SGPT) ≤ 2.5 X
                            institutional ULN OR

                            ≤ 5 X institutional ULN for participants with Gilberts syndrome Albumin
                            >2.5 mg/dL

                         -  Coagulation International Normalized Ratio (INR) or Prothrombin Time
                            (PT) Activated Partial Thromboplastin Time (aPTT) ≤1.5 X institutional
                            ULN unless participant is receiving anticoagulant therapy as long as PT
                            or PTT is within therapeutic range of intended use of anticoagulants
                            ≤1.5 X institutional ULN unless participant is receiving anticoagulant
                            therapy as long as PT or PTT is within therapeutic range of intended
                            use of anticoagulants

          -  Contrast enhanced CT or MRI within 14 days prior to start of study therapy.

          -  An interval of at least 3 weeks (to registration) between prior surgical resection or
             one week for stereotactic biopsy.

          -  An interval of at least 12 weeks from the completion of radiation therapy to
             registration unless there is unequivocal histologic confirmation of tumor progression
             or radiographic progression outside of the prior radiation field.

          -  Participants must have recovered to grade 0 or 1 or pre-treatment baseline from
             clinically significant toxic effects of prior therapy (exceptions include but not
             limited to alopecia, laboratory values not listed per inclusion criteria, and
             lymphopenia which is common after therapy with temozolomide).

          -  From start of study therapy, the following time periods must have elapsed:

               -  5 half-lives from any small molecule investigational agent

               -  4 weeks from cytotoxic therapy (except 23 days for temozolomide, 6 weeks from
                  nitrosoureas, and 7 days from daily administered agents)

               -  6 weeks from antibodies, or 4 weeks (or 5 half-lives, whichever is shorter) from
                  other anti-tumor therapies

               -  No wash-out period required for prior TTF or vaccine therapies

          -  Participants must be planned to undergo surgery that is clinically indicated as
             determined by their care providers (Cohort 2 only).

          -  Female participant of childbearing potential should have a negative urine or serum
             pregnancy within 72 hours prior to registration. If the urine test is positive or
             cannot be confirmed as negative, a serum pregnancy test will be required. Women are
             considered post-menopausal and not of child bearing potential if they have had 12
             months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g.,
             age appropriate, history of vasomotor symptoms) or six months of spontaneous
             amenorrhea with serum FSH levels > 40 mIU/mL and estradiol < 20 pg/mL or have had
             surgical bilateral oophorectomy (with or without hysterectomy) at least six weeks ago.
             In the case of oophorectomy alone, only when the reproductive status of the woman has
             been confirmed by follow up hormone level assessment she considered not of child
             bearing potential.

          -  Women of child-bearing potential (WOCBP), defined as all women physiologically capable
             of becoming pregnant, must use highly effective contraception during study treatment
             and for 120 days after study discontinuation. Highly effective contraception is
             defined as either:

               -  i. True Abstinence: When this is in line with the preferred and usual lifestyle
                  of the participant. Periodic abstinence (e.g., calendar, ovulation,
                  symptothermal, post-ovulation methods) and withdrawal are not acceptable methods
                  of contraception.

               -  ii. Sterilization: Surgical bilateral oophorectomy (with or without hysterectomy)
                  or tubal ligation at least six weeks ago. In case of oophorectomy alone, only
                  when the reproductive status of the woman has been confirmed by follow up hormone
                  level assessment (as described in item 12 above).

               -  iii. Male Partner Sterilization (with the appropriate post-vasectomy
                  documentation of the absence of sperm in the ejaculate). For female participants
                  on the study, the vasectomized male partner should be the sole partner for that
                  participant.

               -  Use of a combination of any two of the following:

                    1. Placement of an intrauterine device (IUD) or intrauterine system (IUS)

                    2. Barrier methods of contraception: Condom or Occlusive cap (diaphragm or
                       cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal
                       suppository

                    3. Appropriate hormonal contraceptives (including any registered and marketed
                       contraceptive agent that contains an estrogen and/or a progestational agent
                       - including oral, subcutaneous, intrauterine, or intramuscular agents)

          -  Male participants should agree to use adequate method of contraception starting with
             the first dose of study therapy through 120 days after the last dose of therapy.

        Exclusion Criteria:

          -  Current or planned participation in a study of an investigational agent or using an
             investigational device.

          -  Has a diagnosis of immunodeficiency.

          -  Has tumor primarily localized to the brainstem or spinal cord.

          -  Has presence of diffuse leptomeningeal disease or extracranial disease.

          -  Has received systemic immunosuppressive treatments, aside from systemic
             corticosteroids as described in Section 3.2.7, (such as methotrexate, chloroquine,
             azathioprine, etc.) within six months of registration.

          -  Has received anti-VEGF or anti-VEGFR targeted agents (e.g. bevacizumab, cediranib,
             aflibercept, vandetanib, XL-184, sunitinib, etc.).

          -  Requires treatment with moderate or high dose systemic corticosteroids defined as
             dexamethasone > 2 mg/day or bioequivalent for at least 3 consecutive days within 2
             weeks of registration.

          -  Has received prior interstitial brachytherapy or stereotactic radiosurgery (Cohort 2
             only).

          -  Has history of known coagulopathy that increases risk of bleeding or a history of
             clinically significant hemorrhage within 12 months of registration.

          -  Has a known history of active TB (Bacillus Tuberculosis).

          -  Has gastrointestinal bleeding or any other hemorrhage/bleeding event CTCAE Grade > 3
             within 6 months of registration.

          -  Has a known additional malignancy that is progressing or requires active treatment
             within 2 years of registration. Exceptions include malignancies treated with surgery
             alone including but not limited to basal cell carcinoma of the skin, squamous cell
             carcinoma of the skin, or in situ cervical cancer that has undergone potentially
             curative therapy.

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e. with use of disease modifying agents, corticosteroids, or immunosuppressive
             drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment. See Section 5.4.3 for additional information on allowed
             corticosteroid dosing.

          -  Has confirmed history or any evidence of active non-infectious pneumonitis.

          -  Has an active infection requiring systemic therapy.

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the participant's
             participation for the full duration of the trial, or is not in the best interest of
             the participant to participate, in the opinion of the treating investigator. Examples
             include but are not limited to symptomatic congestive heart failure, unstable angina
             pectoris, cardiac arrhythmia or psychiatric illness/social situations that would limit
             compliance with study requirements.

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

          -  Is pregnant or breastfeeding or expecting to conceive within the projected duration of
             the trial, starting with the screening visit through 120 days after the last dose of
             trial treatment. It is unknown whether ASP8374 and/or cemiplimab is excreted in human
             milk or may have adverse effects on a fetus in utero. Since many drugs are excreted in
             human milk, and because of the potential for serious adverse reactions in the nursing
             infant or fetus, these participants are not eligible for enrollment.

          -  Has received prior therapy with an anti-TIGIT, anti-PD-1, anti-PD-L1, anti-cytotoxic
             T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab), or any
             other antibody or drug specifically targeting T-cell co-stimulation or checkpoint
             pathways.

          -  Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).

          -  Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA
             [qualitative] is detected).

          -  Has received a live vaccine within 30 days prior to registration.

          -  Has a known hypersensitivity to any of the study therapy products.

          -  Has been previously treated with the PI3K inhibitor idelalisib.