Inclusion Criteria:

• Histologically documented, incurable, locally advanced or metastatic solid malignancies, or NHL without leukemic phase, that has progressed despite standard of care therapy or for which there is no standard therapy of proven clinical benefit
• ECOG performance status of 0 or 1 at screening
• Evaluable or measurable disease per RECIST and/or the following: prostate cancer patients with non-measurable disease are eligible if they have two rising prostate-specific antigen (PSA) levels that meet the PSA Working Group criteria for progression prior to initiation of study treatment; ovarian cancer patients with non-measurable disease are eligible if they have two rising CA-125 levels greater than the ULN >= 2 weeks apart prior to initiation of study treatment.
• Life expectancy >=12 weeks
• Adequate hematologic and organ function within 14 days before initiation of GDC-0980
• Documented willingness to use an effective means of contraception for both men and women while participating in the study

Exclusion Criteria:

• Leptomeningeal disease as the only manifestation of the current malignancy
• History of Type 1 or 2 diabetes mellitus requiring regular medication
• Grade >= 2 hypercholesterolemia or hypertriglyceridemia
• Ejection fraction that is <50% or below the LLN (whichever is higher), as determined by echocardiogram or MUGA scan
• DLCO < 50% of predicted value corrected for hemoglobin and alveolar volume prior to initiation of GDC-0980
• Malabsorption syndrome or other condition that would interfere with enteral absorption
• Known untreated malignancies of the brain or spinal cord, or treated brain metastases that are not radiographically stable for >= 3 months
• Active congestive heart failure or ventricular arrhythmia requiring medication
• Active infection requiring IV antibiotics
• Requirement for any daily supplemental oxygen
• Uncontrolled hypomagnesemia
• Hypercalcemia requiring continued use of bisphosphonate therapy
• Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis
• Uncontrolled ascites requiring frequent paracentesis
• Known HIV infection
• Any other diseases, active or controlled pulmonary dysfunction, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug
• Significant traumatic injury within 4 weeks of Day 1
• Major surgical procedure within 4 weeks prior to initiation of GDC-0980
• For all patients participating in Stage 2: Prior treatment with any PI3K inhibitor, mTOR inhibitor or dual PI3K/mTOR inhibitor. For HNSCC patients, this restriction applies only to any PI3K inhibitor, mTOR inhibitor, or dual PI3K/mTOR inhibitor used in the palliative setting.
• Treatment with chemotherapy, hormonal therapy (except hormone replacement therapy, oral contraceptives, or GnRH agonists or antagonists for prostate cancer), immunotherapy, biologic therapy, radiation therapy (except palliative radiation to bony metastases), or herbal therapy as cancer therapy within 3 weeks prior to initiation of GDC-0980
• Palliative radiation to bony metastases within 2 weeks prior to initiation of GDC-0980
• Need for chronic corticosteroid therapy of >= 10 mg of prednisone per day or an equivalent dose of other anti-inflammatory corticosteroids or immunosuppressant
• Treatment with an investigational agent within 4 weeks prior to initiation of GDC-0980
• Unresolved toxicity from prior therapy except for alopecia and Grade 1 peripheral neuropathy
• Pregnancy or lactation
• For patients participating in DCE-MRI assessments, any contraindication to MRI examination
• For patients with advanced solid tumors or NHL participating in the PPI-effect assessment: Known hypersensitivity to rabeprazole, substituted benzimidazoles, or to any component of the formulation