Personalized Targeted IMMUNOtherapy-based Regimens in Recurrent GASTric Adenocarcinoma (IMMUNOGAST)

Inclusion Criteria: * Histologically and/or cytologically documented recurrent advanced/metastatic gastric or gastroesophageal junction adenocarcinomas\* previously treated with a platinum and fluoropyrimidine-based regimen. \* The gastric or gastroesophageal junction adenocarcinomas that overexpress HER2 should have previously been treated with trastuzumab, except in the case of contraindication. * Patients older than 18 years * Patients with Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1 * Patients must have documented disease progression * Patients who have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 * Accessible tumor lesion (primitive lesion or metastasis) for trial dedicated tumor biopsy. * Left ventricular ejection fraction (LVEF) ≥ 50% by echocardiogram (echo) or multigated acquisition (MUGA) scan within 28 days before day 1 of treatment. * Child-Pugh class A * Patients must have normal organ and marrow function: * Absolute neutrophil count ≥ 1,500/μL, platelets ≥ 100,000/μL, hemoglobin ≥ 9 g/dL * Total bilirubin ≤ 1.5 ULN except subject with documented Gilbert's syndrome, AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional ULN, Serum alkaline phosphatase ≤ 2.5 x ULN. Patients with bone metastases: alkaline phosphatase ≤ 5 x ULN. * Albumin \> 2.5 mg/dL. * Glomerular filtration rate ≥ 60 mL/min as determined by the CKD-EPI equation (or reference methodology such as Iohexol or isotopic technic). * Urine dipstick for proteinuria \< 2+. If urine dipstick is ≥ 2+, 24-hour urine must demonstrate \< 1 g of protein in 24 hours. * Normal blood pressure or adequately treated and controlled hypertension (systolic BP ≤ 140 mmHg and/or diastolic BP ≤ 90 mmHg). * Female patients of childbearing potential must have a negative serum pregnancy test within 8 days of initiating protocol therapy. * Female patients of childbearing potential must agree to use contraceptive methods with a low failure rate (\< 1% per year) during the treatment period and for 6 months after the last dose of study drugs. * Male patients of childbearing potential must agree to use contraceptive methods with a low failure rate during the treatment period and for 6 months after the last dose of study drugs. * Patient is capable of understanding and complying with the protocol and has signed the informed consent document. * Patients affiliated to a social insurance regime. Exclusion Criteria: * Residual toxicity from previous treatment grade ≥1, except for alopecia or peripheral neuropathy grade ≤ 2 * Radiotherapy within 28 days before inclusion, except for palliative radiotherapy if patients recovered from all side effects * Congenital risk of bleeding, or acquired coagulopathy, or curative anti-coagulant therapies (except for low molecular weight heparin). * Active digestive bleeding within 3 months before inclusion * Patients pretreated with one of the experimental drugs, other immune checkpoint inhibitor anti-cancer drugs (anti-PD1, anti-PDL1, anti-CTLA4, …), or with ramucirumab. * Uncontrolled high cholesterol or triglyceride grade ≥ 2 * Uncontrolled intercurrent illness, including, but not limited to, ongoing or active infection, uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, congestive heart failure-New York Heart Association Class III or IV, active ischemic heart disease, myocardial infarction within the previous six months, uncontrolled diabetes mellitus, gastric or duodenal ulceration diagnosed within the previous 6 months, chronic liver or renal disease, or severe malnutrition. * Current peripheral neuropathy of Grade ≥ 3 according to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) v.5.0 * Active, second potentially life-threatening cancer * Other malignancy within the last 5 years except: adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS). Patient with a history of localized malignancy diagnosed over 5 years ago may be eligible provided he completed her adjuvant systemic therapy and remains free of recurrent or metastatic disease. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Major surgery within 28 days before cycle 1, day 1 * Active infection requiring iv antibiotics at day 1 of cycle 1 * Medical condition that requires chronic systemic steroid therapy or on any other form of immunosuppressive medication. For example, patients with autoimmune disease that requires systemic steroids or immunosuppression agents should be excluded. Replacement therapy (eg., thyroxine, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Symptomatic intrinsic lung disease or extensive tumor involvement of the lungs, resulting in dyspnea at rest * Patient is positive for the human immunodeficiency virus (HIV), HepBsAg, or HCV RNA. * Live vaccine within 28 days of planned start of study therapy * History of abdominal fistula, gastrointestinal perforation and/or intra-abdominal abscess within the previous 6 months * History of Type I or Type II diabetes mellitus requiring insulin * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins or Chinese Hamster Ovary (CHO) cell proteins or loperamide drug or excipient * Known hypersensitivity to any of the components of atezolizumab, bevacizumab or ipatasertib * Participation in other interventional clinical research that may interfere with the experimental drugs efficacy * History of severe or life-threatening skin adverse reaction on prior treatment with other immune-stimulatory anticancer agents