Ipatasertib in Combination With Carboplatin, Carboplatin/Paclitaxel, or Capecitabine/Atezolizumab in Treating Patients With Metastatic Triple Negative Breast Cancer

Inclusion Criteria:

* Signed informed consent form
* Ability to comply with the study protocol, in the investigator's judgment
* Histologically or cytologically confirmed triple negative breast cancer defined by estrogen receptor (ER) or progesterone receptor (PR) =\< 10% by immunohistochemistry (IHC) and HER2 negative defined by current American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) guideline
* Disease progression during or following treatment with 0-2 lines of chemotherapy and/or biological targeted therapy in the metastatic setting
* Measurable (Arm C only) or non-measurable (allowed for Arm A or B) but evaluable disease per RECIST version (v)1.1 (Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation.)
* Baseline tissue requirement:

  * A formalin-fixed paraffin-embedded (FFPE) tumor specimen in a paraffin block (preferred) or at least 20 x 5 um slides containing unstained, freshly cut, serial sections must be collected along with an associated pathology report prior to study enrollment
  * If only 10-19 slides are available, the patient may still be eligible for the study, after principal investigator approval has been obtained
  * If archival tumor tissue is unavailable or is determined to be unsuitable for required testing, tumor tissue must be obtained from a biopsy performed at screening
  * A biopsy may also be performed at screening if a patient's archival tissue test results do not meet eligibility criteria
* Eastern Cooperative Oncology Group (ECOG) performance status of 0-1
* Life expectancy \>= 3 months
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (1,500/uL) without granulocyte colony-stimulating factor support (obtained within 14 days prior to initiation of study treatment)
* Platelet count \>= 100 x 10\^9/L (100,000/uL) without transfusion (obtained within 14 days prior to initiation of study treatment)
* Hemoglobin \>= 9 mg/dL (9 mg/dL) (patients may be transfused to meet this criterion) (obtained within 14 days prior to initiation of study treatment)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) (obtained within 14 days prior to initiation of study treatment), with the following exception:

  * Patients with documented liver or bone metastases may have AST and ALT =\< 5 x ULN
* Alkaline phosphatase (ALP) =\< 2 x ULN (obtained within 14 days prior to initiation of study treatment), with the following exceptions:

  * Patients with known liver involvement may have ALP =\< 5 x ULN
  * Patients with known bone involvement may have ALP =\< 7 x upper limit (UL)
* Serum bilirubin =\< 1.5 x ULN (obtained within 14 days prior to initiation of study treatment) with the following exception:

  * Patients with known Gilbert disease: serum bilirubin level =\< 3 x ULN
* Serum creatinine =\< 1.5 x ULN or creatinine clearance \>= 50 mL/min (calculated using the Cockcroft-Gault formula) (obtained within 14 days prior to initiation of study treatment)
* Partial thromboplastin time (PTT) (or activated partial thromboplastin time \[aPTT\]) and international normalized ratio (INR) =\< 1.5 x ULN (except for patients receiving anticoagulation therapy) (obtained within 14 days prior to initiation of study treatment)
* Patients receiving heparin treatment should have a PTT (or aPTT) between 1.5 and 2.5 x ULN (or patient value before starting heparin treatment). Patients receiving coumarin derivatives should have an INR between 2.0 and 3.0 assessed in two consecutive measurements 1 to 4 days apart
* Fasting total glucose =\< 150 mg/dL (obtained within 14 days prior to initiation of study treatment)
* For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 6 months after the last dose of study treatment. Women must refrain from donating eggs during this same period.

  * A woman is considered to be of childbearing potential if she is post-menarcheal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus)
  * Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone- releasing intrauterine devices, and copper intrauterine devices
  * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post ovulation methods) and withdrawal are not acceptable methods of contraception
* For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom, and agreement to refrain from donating sperm, as defined below:

  * With female partners of childbearing potential or pregnant female partners, men must remain abstinent or use a condom during the treatment period and for 6 months after the last dose of study treatment to avoid exposing the embryo. Men must refrain from donating sperm during this same period
  * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post ovulation methods) and withdrawal are not acceptable methods of contraception

Exclusion Criteria:

* Inability to comply with study and follow-up procedures
* \>= grade 3 toxicities from previous treatment, not recovered to =\< grade 2 at study entry
* Prior exposure to PI3K/AKT/mTOR pathway inhibitors including but not limited to everolimus, ipatasertib, gedatolisib or alpelisib etc
* Prior exposure to carboplatin for treatment of metastatic TNBC not allowed; prior treatment of carboplatin as neoadjuvant or adjuvant therapy allowed if last dose of therapy completed \>= 12 months prior to initiation of the current study
* Prior exposure to paclitaxel or nab-paclitaxel for treatment of metastatic TNBC not allowed for carboplatin/paclitaxel arm; prior treatment of paclitaxel or nab-paclitaxel as neoadjuvant or adjuvant therapy allowed if last dose of therapy completed \>= 12 months prior to initiation of the current study
* Prior exposure to capecitabine for treatment of metastatic TNBC not allowed for Arm C; prior treatment of capecitabine as adjuvant therapy allowed if the last dose of therapy completed \>= 12 months prior to initiation of the current study for Arm C
* Prior treatment with immune check point inhibitors for Arm C
* Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, and anti-PD-L1 therapeutic antibodies
* Prior treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 \[IL-2\]) within 4 weeks or 5 drug-elimination half-lives (whichever is longer) prior to initiation of study treatment for Arm C
* Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF-alpha agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions for Arm C:

  * Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study after Medical Monitor confirmation has been obtained
  * Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study
* Active autoimmune disorders requiring steroid dose higher than prednisone 10 mg daily for Arm C
* Active disease or receiving treatment for hepatitis B or C or human immunodeficiency virus (HIV) infection for Arm C
* Receipt of a live, attenuated vaccine within 4 weeks prior to enrollment (start of treatment), during treatment, or within 5 months following the last dose of atezolizumab for Arm C
* Known allergy or hypersensitivity to any component of carboplatin and/or paclitaxel or nab-paclitaxel, or capecitabine (5-FU) formulation (for patients planned for the respective arms)
* Known dihydropyrimidine dehydrogenase (DPD) deficiency in patients selected to receive capecitabine for Arm C
* Known severe allergic reactions to cisplatin or other platinum-containing compounds or mannitol (for patients planned for platinum-containing arms)
* History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins
* Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation
* 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 systemic anti-microbial treatment (including antibiotics, anti-fungals, and anti-viral agents)
* Severe infection within 4 weeks prior to initiation of study treatment, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia
* Known untreated or unstable brain metastasis or leptomeningeal metastasis from metastatic breast cancer
* Uncontrolled tumor-related pain
* Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently)

  * Patients with indwelling catheters (e.g., PleurX) are allowed
* Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL, or corrected calcium \> ULN)
* 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, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren syndrome, Guillain-Barre syndrome, or multiple sclerosis with the following exceptions:

  * Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study.
  * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study.
  * Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met:

    * Rash must cover \< 10% of body surface area
    * Disease is well controlled at baseline and requires only low-potency topical corticosteroids
    * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months
* History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan

  * History of radiation pneumonitis in the radiation field (fibrosis) is permitted.
* Active tuberculosis
* Known HIV infection
* Known clinically significant history of liver disease consistent with Child-Pugh class B or C, including active viral or other hepatitis (e.g., positive for hepatitis B surface antigen \[HBsAg\] or hepatitis C virus \[HCV\] antibody at screening), current drug or alcohol abuse, or cirrhosis

  * Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as having a negative HBsAg test and a positive hepatitis B core antibody \[HBcAb\] test, accompanied by a negative HBV deoxyribonucleic acid \[DNA\] test) are eligible
  * Patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)
* Prior allogeneic stem cell or solid organ transplantation
* 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 during the course of the study

  * Placement of a vascular access device is not considered major surgery
* Pregnant or breastfeeding, or intending to become pregnant during the study or within 28 days after the last dose of ipatasertib, 5 months after the last dose of atezolizumab, and within 6 months after the last dose of paclitaxel, whichever occurs later

  * Women of childbearing potential (who are not postmenopausal with \>= 12 months of non-therapy induced amenorrhea nor surgically sterile) must have a negative serum pregnancy test result either within 96 hours prior to day 1 of cycle 1 treatment
* New York Heart Association class II, III, or IV heart failure; left ventricular ejection fraction \< 50%; or active ventricular arrhythmia requiring medication
* Current unstable angina or history of myocardial infarction within 6 months prior to day 1 of cycle 1 and cerebrovascular accident within 3 months prior to day 1 of cycle 1
* Congenital long QT syndrome or screening QT interval corrected using Fridericia's formula (QTcF) \> 480 milliseconds
* History or presence of an abnormal electrocardiogram (ECG) that is clinically significant in the investigator's opinion (including complete left bundle branch block, second- or third-degree heart block, or evidence of prior myocardial infarction)
* Need for chronic corticosteroid therapy of \>= 10 mg of prednisone per day or an equivalent dose of other anti-inflammatory corticosteroids or immunosuppressants for a chronic disease
* Treatment with approved or investigational cancer therapy within 14 days prior to day 1 of cycle 1
* Patients with a prior diagnosis of malignancy except non-melanomatous skin cancer treated \>= 5 years ago are eligible, provided that they have not received prior taxanes or carboplatin as part of their prior treatment regimen, and that they meet all eligibility criteria
* Any other disease, physical examination finding, or clinical laboratory finding that, in the investigator's opinion, gives reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affec