Inclusion Criteria:

        General:

          -  Eastern Cooperative Oncology Group Performance Status of 0 or 1.

          -  Adequate hematologic and organ function.

          -  For Cohorts 1, 2 and 4: Life expectancy of at least 6 months.

          -  For men and women of child bearing potential: agreement to remain abstinent or use
             protocol defined contraceptive measures during the treatment period and for at least
             28 days after the last dose of ipatasertib, 6 months after the last dose of
             paclitaxel, nab-paclitaxel, or doxorubicin, and 12 months after the last dose of
             cyclophosphamide, and 5 months after the last dose of atezolizumab, whichever occurs
             later along with refraining from donating sperm or eggs during this same period.

        Disease-specific:

          -  For Cohorts 1, 2 and 4: histologically documented TNBC that is locally advanced or
             metastatic and is not amenable to resection with curative intent.

          -  For Cohort 2: disease progression following one or two lines of systemic therapy for
             inoperable locally advanced or metastatic TNBC.

          -  For Cohorts 1, 2 and 4: measurable disease according to RECIST v1.1 criteria.

          -  For Cohort 2: Treated brain or spinal cord metastases are allowed if participants have
             stable disease and are not on steroid treatment.

          -  For Cohort 3: histologically documented TNBC with a primary breast tumour size of > 2
             cm by at least one radiographic or clinical measurement and disease stage at
             presentation of cT2-4 cN0-3 cM0.

          -  For Cohort 3: participant agreement to undergo appropriate surgical management,
             including axillary lymph node surgery and partial or total mastectomy, after
             completion of neoadjuvant treatment.

          -  For Cohort 4: participants must have centrally confirmed PD-L1-positive tumour.

        Exclusion Criteria:

        General:

          -  History of malabsorption syndrome or other condition that would interfere with enteral
             absorption or results in the inability or unwillingness to swallow pills.

          -  Active infection requiring antibiotics.

          -  History of or current evidence of HIV infection.

          -  Known clinically significant history of liver disease.

          -  Major surgical procedure, open biopsy, or significant traumatic injury within 28 days
             prior to Day 1 of Cycle 1 or anticipation of need for a major surgical procedure
             (other than anticipated breast surgery for Cohort 3) during the course of the study.

          -  Pregnant or breastfeeding.

          -  New York Heart Association (NYHA) Class II, III, or IV heart failure; left ventricular
             ejection fraction < 50%; or active ventricular arrhythmia requiring medication.

          -  Treatment with approved or investigational cancer therapy within 14 days prior to Day
             1 of Cycle 1.

          -  Prior treatment with an Akt inhibitor.

        Disease-specific:

          -  For Cohorts 1 and 4: history of or known presence of brain or spinal cord metastases.

          -  For Cohorts 1 and 4: participants who have received previous systemic therapy for
             inoperable locally advanced or metastatic TNBC, including chemotherapy, immune
             checkpoint inhibitors, or targeted agents.

          -  Unresolved, clinically significant toxicity from prior therapy, except for alopecia
             and Grade 1 peripheral neuropathy.

          -  Participants who have received palliative radiation treatment to peripheral sites
             (e.g., bone metastases) for pain control and whose last treatment was completed 14
             days prior to Day 1 of Cycle 1 and have recovered from all acute, reversible effects.

          -  Uncontrolled pleural effusion, pericardial effusion, or ascites.

          -  Uncontrolled tumor related complications.

          -  Uncontrolled hypercalcaemia or symptomatic hypercalcaemia requiring continued use of
             bisphosphonate therapy.

          -  Malignancies other than breast cancer within 5 years prior to Day 1 of Cycle 1.

          -  For Cohort 3, participants with the following are excluded: [1] prior history of
             invasive breast cancer; [2] prior systemic therapy for treatment and/or prevention of
             invasive breast cancer; [3] previous therapy with anthracyclines or taxanes for any
             malignancy; [4] bilateral breast cancer; [5] undergone incisional and/or excisional
             biopsy of primary tumor and/or axillary lymph nodes; [6] undergone axillary lymph node
             dissection (ALND) prior to initiation of neoadjuvant therapy; [6] history of other
             malignancy within 5 years prior to screening; [7] history of cerebrovascular accident
             within 12 months prior to initiation of study treatment; [8] cardiopulmonary
             dysfunction; [9] known allergy or hypersensitivity to the components of
             cyclophosphamide/doxorubicin formulations and filgrastim or pegfilgrastim
             formulations; [10] severe infection within 4 weeks prior to initiation of study
             treatment; [11] treatment with therapeutic oral or IV (Intravenous) antibiotics within
             2 weeks prior to initiation of study treatment and [12] prior treatment with CD137
             agonists or immune checkpoint - blockade therapies.

        Ipatasertib-specific:

          -  History of Type I or Type II diabetes mellitus requiring insulin.

          -  Grade >= 2 uncontrolled or untreated hypercholesterolemia or hypertriglyceridemia.

          -  History of or active inflammatory bowel disease or active bowel inflammation.

          -  Clinically significant lung disease.

          -  Treatment with strong CYP3A inhibitors or strong CYP3A inducers.

        Atezolizumab-specific:

          -  Active or history of autoimmune disease or immune deficiency.

          -  History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis
             obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active
             pneumonitis on screening chest computed tomography (CT) scan.

          -  Prior allogeneic stem cell or solid organ transplantation.

          -  Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study
             treatment, or anticipation of need for such a vaccine during treatment with
             atezolizumab or within 5 months after the last dose of atezolizumab.

          -  History of hypersensitivity reactions to study drug or any component of the study drug
             formulation.

          -  Treatment with systemic immunostimulatory agents and immunosuppressive medication
             treatment, or anticipation of need for systemic immunosuppressive medication during
             the course of the study.

        Paclitaxel-specific:

        - Grade >= 2 peripheral neuropathy.