Gamma-Secretase/Notch Signalling Pathway Inhibitor RO4929097, Paclitaxel, and Carboplatin Before Surgery in Treating Patients With Stage II or Stage III Triple-Negative Breast Cancer

Inclusion Criteria:

* The patients must have histologically confirmed breast cancer that is human epidermal growth factor receptor 2 (Her-2) negative (immunohistochemistry \[IHC\] 0-1+ patients are eligible without fluorescence in situ hybridization \[FISH\]; IHC2+ patients are eligible with negative FISH; if FISH only is done HER2/chromosome enumeration probe \[CEP\]17 \< 2.0); the invasive tumor must be hormone receptor negative defined as both estrogen receptor and progesterone receptor IHC staining present in less than 10% of invasive cancer cells
* Eligible patients must have clinical stage II-III breast cancer; patients with inflammatory breast cancer are not eligible
* Patients must have clinically or radiographically measurable primary breast tumor that measures \>= 2.0 cm
* No prior treatment including radiation therapy, chemotherapy or biotherapy for the currently diagnosed breast cancer is allowed
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \> 80%)
* Hemoglobin \>= 9 g/dL
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \> 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin within normal institutional limits
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 X institutional upper limit of normal
* Creatinine \< 1.5 X institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Women of childbearing potential and men must use two forms of contraception (i.e., barrier contraception and one other method of contraception) at least 4 weeks prior to study entry, for the duration of study participation, and for at least 12 months post-treatment; should a woman become pregnant or suspect she is pregnant while she or her partner are participating in this study and for 12 months after study participation, the patient should inform the treating physician immediately
* Pregnancy testing; women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 10-14 days and within 24 hours prior to the first dose of RO4929097 (serum or urine); a pregnancy test (serum or urine) will be administered every 4 weeks if their menstrual cycles are regular or every 2 weeks if their cycles are irregular while on study within the 24-hour period prior to the administration of RO4929097; a positive urine test must be confirmed by a serum pregnancy test; prior to dispensing RO4929097, the investigator must confirm and document the patient's use of two contraceptive methods, dates of negative pregnancy test, and confirm the patient's understanding of the teratogenic potential of RO4929097
* Female patients of childbearing potential are defined as follows:

  * Patients with regular menses
  * Patients, after menarche with amenorrhea, irregular cycles, or using a contraceptive method that precludes withdrawal bleeding
  * Women who have had tubal ligation
* Female patients may be considered to NOT be of childbearing potential for the following reasons:

  * The patient has undergone total abdominal hysterectomy with bilateral salpingo-oophorectomy or bilateral oophorectomy
  * The patient is medically confirmed to be menopausal (no menstrual period) for 24 consecutive months
* Ability to swallow pills
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients may not be receiving any other investigational agents
* Patients with inflammatory breast cancer are not eligible
* Prior history of invasive breast cancer treated with systemic chemotherapy (patients with a history of ductal carcinoma in situ \[DCIS\] and lobular carcinoma in situ \[LCIS\] are eligible)
* Other malignancies unless the patient is considered to be disease-free for 5 or more years prior to study registration; patients with the following cancers are eligible if diagnosed and treated within the past 5 years: carcinoma in situ of the cervix, carcinoma in situ of the colon, melanoma in situ, and basal and squamous cell carcinoma of the skin
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to RO4929097 or other agents used in the study
* Patients taking medications with narrow therapeutic indices that are metabolized by cytochrome P450 (CYP450), including warfarin sodium (Coumadin) are ineligible
* Preclinical studies indicate that RO4929097 is a substrate of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) and inducer of CYP3A4 enzyme activity; caution should be exercised when dosing RO4929097 concurrently with CYP3A4 substrates, inducers, and/or inhibitors; furthermore, patients who are taking concurrent medications that are strong inducers/inhibitors or substrates of CYP3A4 should be switched to alternative medications to minimize any potential risk; if such patients cannot be switched to alternative medications, they will be ineligible to participate in this study
* Preclinical studies indicate that RO4929097 is a substrate of cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8) and inducer of CYP2C8 enzyme activity; caution should be exercised when dosing RO4929097 concurrently with CYP2C8 substrates, inducers, and/or inhibitors; furthermore, patients who are taking concurrent medications that are strong inducers/inhibitors or substrates of CYP2C8 should be switched to alternative medications to minimize any potential risk; if such patients cannot be switched to alternative medications, they will be ineligible to participate in this study
* Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption; patients must be able to swallow tablets
* Patients who are serologically positive for hepatitis A, B or C, or have a history of liver disease, other forms of hepatitis or cirrhosis are ineligible
* Uncontrolled electrolyte abnormalities including hypocalcemia, hypomagnesemia,and hypokalemia; symptomatic congestive heart failure, unstable angina pectoris, and a history of torsades de pointes or other significant cardiac arrhythmias
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with RO4929097
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
* Cardiovascular: baseline corrected QT interval (QTc) \> 450 msec in males or QTc \> 470 msec in females
* A requirement for antiarrhythmics or other medications known to prolong QTc
* Patients who have not recovered to \< Common Terminology Criteria for Adverse Events (CTCAE) grade 2 toxicities related to prior therapy are not eligible to participate in this study
* Peripheral neuropathy of grade 2 or higher