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:  Placement of an intrauterine device (IUD) or intrauterine system (IUS) Barrier methods of contraception: Condom or Occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository 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.