Women's MoonShot: Neoadjuvant Treatment With PaCT for Patients With Locally Advanced TNBC

Inclusion Criteria:

* Patients must have an intact evaluable primary tumor or biopsy proven axillary node involvement with at least 1.0 centimeter (cm) smallest dimension based on imaging after neoadjuvant anthracycline-based chemotherapy and prior to initiation of neoadjuvant chemotherapy under this protocol; baseline measurements and evaluations must be obtained within 4 weeks of registration to the study; all areas of disease should be recorded in order to assess response and uniformity of response to therapy
* 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 positive (+) by IHC or 2+, fluorescence in situ hybridization (FISH) \< 2, gene copy number \< 4
* Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Patients must have received at least one dose of an anthracycline based neoadjuvant regimen; patients are eligible if therapy was discontinued due to disease progression or therapy intolerance
* Baseline multi-gated acquisition (MUGA) or echocardiogram showing left ventricular ejection fraction (LVEF) \>= 50% within 6 weeks prior to initiation of neoadjuvant chemotherapy
* Serum creatinine =\< 1.5 mg/dl
* Creatinine clearance (CrCl) \>= 50 mL/min calculated by the Cockcroft-Gault method
* Absolute neutrophil count (ANC) \>= 1500/mm\^3
* Platelets \>= 100,000/mm\^3
* Hemoglobin \>= 9.0 g/dL
* Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 3.0 x upper limit of normal
* Alkaline phosphatase (Alp) =\< 2.5 x upper limit of normal (ULN)
* Total bilirubin =\< 1.5 x ULN
* Signed informed consent

Exclusion Criteria:

* Patient is unwilling or unable to sign and date the Institutional Review Board (IRB) approved informed consent
* Patients with less than a 1.0 cm measurable residual disease after neoadjuvant anthracycline based chemotherapy
* Women that are pregnant or lactating
* Patients with a history of prior malignancy within 5 years of study entry with the exception of curatively treated non-melanomatous skin cancer or carcinoma in situ of the cervix or breast
* Patients with a history of stage IV or metastatic disease
* Any serious medical illness, other than that treated by this study, which would limit survival to less than 1 month or psychiatric illness which would limit informed consent
* Known positive test(s) for human immunodeficiency virus infection, hepatitis C virus, acute or chronic active hepatitis B infection
* Patients with a peripheral neuropathy \> grade 1
* Patients with a history of serious cardiac events defined as: New York Heart Association class 3 or 4 heart failure, or history of myocardial infarction, unstable angina or cerebrovascular accident (CVA) within 6 months of protocol registration
* Patients with a history of PR prolongation or atrioventricular (AV) block
* Patients with a history of prior therapy with paclitaxel and/or carboplatin
* Patients who have received a cumulative dose of doxorubicin of greater than 360 mg/m\^2 or epirubicin of greater than 640 mg/m\^2
* Patients who concurrently use hormonal therapy and/or concurrent radiation therapy
* Patients who had prior radiation therapy of the primary breast carcinoma or axillary lymph nodes
* 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; 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
* Negative serum or urine pregnancy test for women within 72 hours of receiving the first dose of the study medication for women of childbearing potential