• Patients must have pathologically confirmed HNSCC (including tumors of the oropharynx, hypopharynx, larynx, oral cavity, nasal cavity, maxillary and other paranasal sinuses, and unknown primary of the head and neck), with measurable disease as per RECIST 1.1

• Oropharyngeal and unknown primary squamous cell cancers must test for human papilloma virus (HPV), for example by p16 immunohistochemistry (IHC), in situ hybridization (ISH), or polymerase chain reaction (PCR). HPV testing is not required for other HNSCC primary tumor sites

‣ For the dose escalation phase only (not the expansion phase), patients with p16-positive tumors are eligible if clinical stage III (cT4 or cN3, M0) according to the American Joint Committee on Cancer (AJCC)/TNM Staging System, 8th edition (Ed.)

⁃ For both the dose escalation and expansion phases, patients with p16-negative (or not tested) tumors are eligible if clinical stage III-IVB (locally advanced but non-metastatic) according to the AJCC/TNM Staging System, 8th Ed.

• Must be candidate for concurrent, definitive cisplatin and radiation therapy as judged by the treating physician

• Able to swallow tablets at the time of enrollment

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of ipatasertib in combination with chemoradiation in patients \< 18 years of age, children are excluded from this study

• Eastern Cooperative Oncology Group (ECOG) performance status 0-1

• Life expectancy of greater than 3 months

• Absolute neutrophil count \>= 3000/mcL

• Hemoglobin \>= 10 g/dL

• Platelets \>= 150,000/mcL

• Serum albumin \>= 3 g/dL

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN / 2 x institutional ULN

• Alkaline phosphatase (ALP) =\< 2.0 x institutional ULN

• Partial thromboplastin time (PTT) (or activated \[a\]PTT) and international normalized ratio (INR) =\< 1.5 institutional ULN (except for patients receiving anticoagulation therapy)

• Creatinine clearance (CLcr) \> 60 mL/min

‣ For this calculation, use the Cockroft-Gault formula

• Fasting glucose =\< 150 mg/dL (8.3 mmol/L) and (when indicated) glycosylated hemoglobin (HbA1c ) =\< 7.5% (58 mmol/mol)

• Human immunodeficiency virus (HIV)-infected patients are eligible if on effective anti-retroviral therapy with undetectable viral load within 6 months

• Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as having a negative hepatitis B virus surface antigen \[HBsAg\] test and a positive hepatitis B core antibody \[HBcAb\] test, accompanied by a negative HBV deoxyribonucleic acid \[DNA\] test) are eligible. Patients with chronic HBV infection are eligible if the HBV viral load is undetectable on suppressive therapy, if indicated. Patients undergoing current treatment with anti-viral therapy for HBV are ineligible

• Patients with a history of hepatitis C virus (HCV) infection are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). Patients with HCV infection who are currently on treatment are eligible if they have an undetectable HCV viral load

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

• The effects of ipatasertib on the developing human fetus are unknown. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for at least 28 days after the last dose of ipatasertib and agreement to refrain from donating eggs during this same period. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm during the treatment period and for 28 days after the last dose of ipatasertib

• Ability to understand and the willingness to sign a written informed consent document

• For the expansion cohort only, patients must agree to undergo mandatory on-treatment biopsies, and have tumors amenable to on-treatment biopsies. This is not applicable to the dose escalation cohort where no on-treatment biopsies are obtained