Inclusion Criteria

          -  Ability to comply with the study protocol, in the investigator's judgment

          -  Willingness and ability to comply with scheduled visits, treatment plans, laboratory
             tests, and other study procedures, including the completion of patient-reported
             outcome questionnaires

          -  Histological diagnosis of high-grade serous or Grade 2 or Grade 3 endometrioid
             epithelial ovarian, fallopian tube, or primary peritoneal cancer

          -  Previous treatment with a minimum of one and a maximum of two prior platinum based
             treatment regimens

          -  Platinum-sensitive disease

          -  Availability of tumor biopsy tissue prior to first dose of study treatment with
             confirmation by the central laboratory that the sample is not only of adequate quality
             but also assignable to a molecularly defined subgroup based on breast cancer
             susceptibility gene (BRCA) and loss of heterozygosity (LOH) status

          -  Measurable disease, as defined by Response Evaluation Criteria in Solid Tumors,
             version 1.1 (RECIST v1.1)

          -  Adequate hematologic and organ function

          -  Eastern Cooperative Oncology Group Performance Status of 0 or 1

          -  Life expectancy of at least 12 weeks

          -  Resolved or stabilized toxicities resulting from previous therapy to Grade 1

          -  Negative HIV test at screening

          -  Negative hepatitis B surface antigen and total hepatitis B core antibody (HBcAb) test,
             or positive total HBcAb test followed by quantitative hepatitis B virus (HBV) DNA <
             500 IU/mL test at screening

          -  Negative hepatitis C virus (HCV) antibody test, or positive HCV antibody test followed
             by a negative HCV RNA test at screening

          -  For women of childbearing potential: Women must remain abstinent or use two
             contraceptive methods with a failure rate of <1% per year during the treatment period
             and for at least 3 months after the last dose of cobimetinib, 6 months after the last
             dose of niraparib, and 5 months after the last dose of atezolizumab. Women must
             refrain from donating eggs during this same period

        Exclusion Criteria

          -  Prior treatment with mitogen-activated protein kinase inhibitor, polyadenosine
             diphosphate-ribose polymerase inhibitor, or immune checkpoint inhibitor therapies

          -  Prior chemotherapy, hormonal therapy, radiotherapy, antibody therapy, or other
             immunotherapy, gene therapy, vaccine therapy, or treatment with experimental drugs
             within 14 days prior to first dose of study treatment

          -  Treatment with systemic immunostimulatory agents within 28 days or 5 half-lives of the
             drug prior to initiation of study treatment

          -  Treatment with systemic immunosuppressive medication 14 days prior to initiation of
             study treatment, or anticipation of need for systemic immunosuppressive medication
             during the study

          -  History of other malignancy that could affect compliance with the protocol or
             interpretation of results, or known to have potentially fatal outcome

          -  Symptomatic and/or untreated central nervous system metastases

          -  Surgical procedure, significant traumatic injury within 14 days prior to enrollment,
             or anticipation of need for major surgical procedure during the study

          -  Minor surgical procedure within 3 days

          -  History or evidence of retinal pathology on ophthalmic examination

          -  Left ventricular ejection fraction below institutional lower limit of normal

          -  History of clinically significant cardiovascular dysfunction

          -  History of idiopathic pulmonary fibrosis, organizing pneumonia, drug-induced
             pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on the
             screening chest computed tomography scan

          -  History or evidence of inherited bleeding diathesis or significant coagulopathy at
             risk for bleeding

          -  History of severe allergic, anaphylactic, or other hypersensitivity reactions to
             chimeric or humanized antibodies or fusion proteins, or to any component of the
             atezolizumab formulation

          -  Known allergy or hypersensitivity to any component of the cobimetinib or niraparib
             formulation

          -  Active or history of autoimmune disease or immune deficiency including, but not
             limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus
             erythematosus, rheumatoid arthritis, inflammatory bowel disease, anti-phospholipid
             antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barre syndrome,
             or multiple sclerosis

          -  Uncontrolled serious medical or psychiatric illness

          -  History of malabsorption or other condition that would interfere with absorption of
             oral study drugs, including preexisting duodenal stent or ongoing intestinal
             obstruction

          -  Active tuberculosis

          -  Severe infection within 14 days prior to initiation of study treatment, including, but
             not limited to, hospitalization for complications of infection, bacteremia, or severe
             pneumonia

          -  Treatment with therapeutic oral or IV antibiotics within 7 days prior to initiation of
             study treatment

          -  Treatment with a live, attenuated influenza vaccine within 28 days prior to study
             treatment initiation, at any time during the study, and for at least 5 months after
             the last dose of study drug

          -  Any other disease, metabolic dysfunction, physical examination finding, or clinical
             laboratory finding that contraindicates the use of an investigational drug, may affect
             the interpretation of the results, or may render the patient at high risk from
             treatment complications

          -  Previous treatment with strong CYP3A inhibitors (such as ketoconazole and
             clarithromycin), strong CYP3A inducers (such as carbamazepine and phenytoin), and
             moderate CYP3A inducers (such as efavirenz, modafinil) within 7 days prior to the
             initiation of study treatment or with ongoing requirements for these medications

          -  Pregnancy or breastfeeding, or intention to become pregnant during the study