Inclusion Criteria:
Solid tumor that is metastatic, locally advanced or recurrent
Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
Life expectancy greater than or equal to (>/=) 12 weeks
Measurable disease, as defined by RECIST v 1.1
Adequate hematologic and end organ function
Use of highly effective contraception
Histological tumor tissue specimen
Participants enrolling in the indication-specific expansion cohorts in Stage 2 must consent to tumor biopsies and must have one of the following types of cancer:
- Metatastic colorectal cancer
- Non-small cell lung cancer
- Melanoma
Exclusion Criteria:
Cancer-Specific Exclusion Criteria:
- Any approved anti-cancer therapy, including chemotherapy, or hormonal therapy within 3 weeks prior to initiation of study treatment
- Treatment with any other investigational agent or participation in another clinical trial with therapeutic intent within 28 days prior to enrollment
- Known active or untreated central nervous system (CNS) metastases
- Leptomeningeal disease
- Uncontrolled tumor-related pain or uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent (once monthly or more frequently) drainage procedures
- Uncontrolled hypercalcemia or symptomatic hypercalcemia requiring continued use of bisphosphonate therapy or denosumab
General Medical Exclusion Criteria:
- Pregnant and lactating women
- History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins
- Known hypersensitivity to biopharmaceuticals produced in Chinese hamster ovary cell or any component of the atezolizumab formulation
- History of autoimmune disease
- Participants with prior allogeneic stem cell or solid organ transplantation
- Positive test for human immunodeficiency virus (HIV)
- Participants with active hepatitis B, hepatitis C, or tuberculosis
- Severe infections within 4 weeks prior to Cycle 1 Day 1
- Signs or symptoms of infection within 2 weeks prior to Cycle 1 Day 1
- Received therapeutic oral or IV antibiotics within 2 weeks prior to Cycle 1 Day 1
- Significant cardiovascular disease
- Major surgical procedure other than for diagnosis within 28 days prior to Cycle 1 Day 1 or anticipation of need for a major surgical procedure during the course of the study
- Administration of a live, attenuated vaccine within 4 weeks before Cycle 1 Day 1
Exclusion Criteria Unique to Cobimetinib:
- History of prior significant toxicity from another mitogen-activated protein kinase (MEK) pathway inhibitor requiring discontinuation of treatment
- Allergy or hypersensitivity to components of the cobimetinib formulations
- History of congenital long QT syndrome or corrected QT interval (QTc) greater than (>) 450 milliseconds at screening
- Left ventricular ejection fraction (LVEF) below institutional lower limit of normal (LLN) or below 50%, whichever is lower, as determined by echocardiogram or Multi Gated Acquisition Scan (MUGA) scan
- History of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment, central serous chorioretinopathy (CSCR), retinal vein occlusion (RVO), or neovascular macular degeneration
- History of malabsorption syndrome or other condition that would interfere with enteral absorption
Exclusion Criteria Related to Medications:
- Prior treatment with clusters of differentiation (CD) 137 agonists or immune checkpoint blockade therapies, systemic immunostimulatory agents, or systemic immunosuppressive medications