Liposomal Doxorubicin, Bevacizumab, and Everolimus in Patients With Locally Advanced TNBC With Tumors Predicted Insensitive to Standard Chemotherapy; A Moonshot Initiative

Inclusion Criteria:

* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Confirmed invasive triple-negative breast cancer defined as estrogen receptor (ER) \< 10%; progesterone receptor (PR) \< 10% by immunohistochemistry (IHC) and human epidermal growth factor receptor 2 (HER2) 0-1+ (by IHC), or 2+ (fluorescence in situ hybridization \[FISH\] \< 2, gene copy number \< 4)
* Primary tumor sample collected before NACT started and
* Undergone molecular testing for integral biomarkers including immunohistochemical staining; the tumor must have evidence of mesenchymal differentiation defined as metaplastic breast cancer, or vimentin \>= 50% by IHC
* Received at least one dose of an anthracycline-based NACT; patients are eligible if therapy was discontinued due to disease progression or therapy intolerance
* At least 1.0 cm of measurable residual disease after neoadjuvant anthracycline-based chemotherapy
* Baseline multi-gated acquisition (MUGA) scan or echocardiogram showing left ventricular ejection fraction (LVEF) \>= 50% at least 6 weeks prior to initiation of NACT
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L
* Platelets \>= 100 x 10\^9/L
* Hemoglobin (Hb) \> 9 g/dL
* Total serum bilirubin =\< 2.0 mg/dL
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN) (=\< 5 x ULN in patients with liver metastases)
* International normalized ratio (INR) =\< 2
* Serum creatinine =\< 1.5 x ULN
* Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L, AND fasting triglycerides =\< 2.5 x ULN; NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication
* Signed informed consent obtained prior to any screening procedures

Exclusion Criteria:

* Pregnant or lactating woman
* Presence of metastatic disease
* Prior therapy with bevacizumab, liposomal doxorubicin, or everolimus
* Prior radiation therapy of the primary breast carcinoma or axillary lymph nodes
* Patients who have a history of another primary malignancy, with the exceptions of: non-melanoma skin cancer, and carcinoma in situ of the cervix, uterus, or breast from which the patient has been disease free for =\< 3 years
* Prior cumulative dose of doxorubicin of greater than 360 mg/m\^2 or epirubicin of greater than 640 mg/m\^2
* Any serious medical illness, other than treated by this study, which would limit survival to less than 1 month or psychiatric illness which would limit informed consent
* Patients with history of serious cardiac events defined as: New York Heart Association class 3 or 4 heart failure, history of myocardial infarction, unstable angina, or cardiovascular accident (CVA) within 6 months of protocol registration; history of PR prolongation or atrioventricular (AV) block
* Known intolerance or hypersensitivity to rapamycin analogs (e.g. sirolimus, temsirolimus)
* Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral everolimus
* Uncontrolled diabetes mellitus as defined by hemoglobin A1c (HbA1c) \> 8% despite adequate therapy; patients with a known history of impaired fasting glucose or diabetes mellitus (DM) may be included, however blood glucose and antidiabetic treatment must be monitored closely throughout the trial and adjusted as necessary
* Patients who have any severe and/or uncontrolled medical conditions such as: a. serious uncontrolled cardiac arrhythmia, or any other clinically significant cardiac disease b. active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and active and chronic hepatitis (i.e. quantifiable hepatitis B virus \[HBV\]-deoxyribonucleic acid \[DNA\] and/or positive surface antigen of the hepatitis B virus \[HBsAg\], quantifiable hepatitis C virus \[HCV\]-ribonucleic acid \[RNA\]), c. known severely impaired lung function (spirometry and Diffusing capacity of the lungs for carbon monoxide \[DLCO\] 50% or less of normal and oxygen (O2) saturation 88% or less at rest on room air), d. active, bleeding diathesis; e. Moderate or severe hepatic impairment (Child-Pugh B or C)
* Chronic treatment with corticosteroids or other immunosuppressive agents; topical or inhaled corticosteroids are allowed
* Known history of human immunodeficiency virus (HIV) seropositivity
* Patients who have received live attenuated vaccines within 1 week of start of everolimus and during the study; patient should also avoid close contact with others who have received live attenuated vaccines; examples of live attenuated vaccines include intranasal influenza, measles, mumps, rubella, oral polio, bacillus Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines
* Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study
* Patients who are currently part of or have participated in any clinical investigation with an investigational drug within 1 month prior to dosing
* Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must use highly effective methods of contraception during the study and 8 weeks after; highly effective contraception methods include combination of any two of the following:

  * Placement of an intrauterine device (IUD) or intrauterine system (IUS);
  * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository;
  * Total abstinence or;
  * Male/female sterilization.
  * Note: Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to treatment; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential
* Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 8 weeks after the end of treatment