A Study to Evaluate the Safety, Pharmacokinetics and Clinical Activity of RO6870810 and Atezolizumab (PD-L1 Antibody) in Participants With Advanced Ovarian Cancer or Triple Negative Breast Cancer

Inclusion Criteria:- * Groups 1 and 2: Participants with histologically confirmed advanced ovarian cancer or triple negative breast cancer who in the opinion of the Investigator are appropriate for this study * Group 3: Participants with histologically confirmed TNBC who have received either one or 2 prior systemic treatments for metastatic breast cancer, and who have documented disease progression on or after the most recent treatment * Group 4: Recurrent ovarian cancer participant who have received no more than two prior lines of platinum therapy in the recurrent setting and have progressed within 9 months from the last platinum containing regimen * Measurable disease by RECIST criteria version 1.1 prior to study drug administration * Performance status of 0 or 1 on the eastern Cooperative Oncology Group (ECOG) scale * Life expectancy, in the opinion of the Investigator, of at least 3 months * Disease-free of active second/secondary or prior malignancies for =\> 2 years with the exception of squamous cell carcinoma of the skin, or carcinoma in situ of the cervix or breast * Willing to provide the protocol specified tumor biopsies * Acceptable hematologic status, liver and renal function * Groups 1 and 2: Participants who have received prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, and anti-PD-L1 therapeutic antibodies, may be enrolled, provided the following requirements are met: * Minimum of 5 months from the last dose of anti-PD-1, anti-CTLA-4, anti-PD- L1 or CD137 agonist treatment * No history of severe immune-related adverse effects from CD137 agonist, anti-CTLA-4, anti-PD-1 or anti-PD-L1 (NCI CTCAE Grade 3 and 4). Any toxicity related to the therapy must have resolved completely, no residual toxicity as assessed by NCI CTCAE (v4.03) * Agree to use protocol defined methods of contraception - For all participants, the reliability of sexual abstinence must be evaluated in relation to the duration of the clinical study and the preferred and usual lifestyle of the participant. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not acceptable methods of contraception Exclusion Criteria: * Participants with history of prior malignancy except solid tumor treated curatively more than 3 years ago without evidence of recurrence * Asymptomatic or symptomatic, untreated, or actively progressing central nervous system (CNS) metastases * History of leptomeningeal disease * Uncontrolled tumor-related pain * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures. Participants with indwelling catheters are allowed. * Uncontrolled or symptomatic hypercalcemia * New York Heart Association Class III or IV cardiac disease, pericarditis, myocardial infarction within the past 6 months, unstable arrhythmia * Fredericia-corrected QT interval (QTcF) \> 470 milli seconds (msec) (female) or \> 450 msec (male), or history of congenital long QT syndrome. Any electrocardiogram (ECG) abnormality, including pericarditis, which in the opinion of the Investigator would preclude safe participation in the study. * Active, uncontrolled bacterial, viral, or fungal infections within 7 days of study entry requiring systemic therapy. Participants with active TB infection are excluded from the study. * Known clinically important respiratory impairment * History of major organ transplant * History of an autologous or allogeneic bone marrow transplant * Serious non-malignant disease that could compromise protocol objectives in the opinion of the Investigator and/or the Sponsor * Pregnant or nursing women * Any systemic anticancer therapy within 3 weeks prior to Cycle 1 Day 1 * Any radiation treatment to metastatic site within \<= 14 days of Cycle 1 Day 1 * Major surgical procedure, open biopsy, or significant traumatic injury within 30 days prior to Cycle 1 Day 1 or anticipation of need for major surgical procedure during the course of the study * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric, human or humanized antibodies or fusion proteins * Known hypersensitivity or allergy to biopharmaceuticals produced in Chinese hamster ovary cells or any component of the atezolizumab formulation * Active or history of autoimmune disease * History of idiopathic pulmonary fibrosis (including pneumonitis), drug-induced pneumonitis, organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia), or evidence of active pneumonitis on screening chest computed tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted * Positive test for Human immunodeficiency virus (HIV) * Active hepatitis B or hepatitis C * Receipt of a live, attenuated vaccine within 4 weeks prior to randomization or anticipation that such a live, attenuated vaccine will be required during the study * Treatment with investigational therapy within 28 days prior to initiation of study treatment * Treatment with therapeutic oral or IV antibiotics within 2 weeks prior to initiation of study treatment * Consumption of agents which strongly inhibit CYP3A4 enzyme, within 7 days prior to the first dose of study treatment and during the study * Consumption of agents which strongly induce CYP3A4 enzyme, within 14 days prior to the first dose of study treatment and during the study * Treatment with systemic immuno-stimulatory agents within 4 weeks or five half-lives of the drug (whichever is shorter) prior to the first dose of study treatment * Treatment with systemic corticosteroids or other systemic immunosuppressive medications within 2 weeks prior to the first dose of study treatment, or, anticipated requirement for systemic immunosuppressive medications during the trial * History of allergic reactions attributed to components of the formulated product(s) * Unwillingness or inability to comply with procedures required in this protocol