Neratinib and Paclitaxel With or Without Pertuzumab and Trastuzumab Before Combination Chemotherapy in Treating Patients With Metastatic or Locally Advanced Breast Cancer

Inclusion Criteria

• •Histological confirmation of breast cancer
• •Able to provide written informed consent for the trial
• •Performance status of =\< 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale
• •Able to swallow oral medication
• •Left ventricular ejection fraction (LVEF) assessment by 2-dimensional (D) echocardiogram or multi-gated acquisition (MUGA) scan performed within 90 days prior to registration must be \>= 50%
• •Absolute neutrophil count \>= 1,500 /uL
• •Platelets \>= 100,000 /uL
• •Hemoglobin \>= 9 g/dL
• •Creatinine clearance \>= 50 ml/min
• •Total bilirubin =\< 1.5 X upper limit of normal (ULN), for patients with congenital unconjugated hyperbilirubinemia (Crigler-Najjar syndrome type 1 and 2, Gilbert syndrome) that transient hyperbilirubinemia can occur due to physiological condition, as long as there is clear documentation of diagnosis, allowed to be enrolled if direct (conjugated) bilirubin is =\< 1.5 X ULN
• •Alanine aminotransferase and aspartate aminotransferase =\< 2.5 X ULN except in patients with aspartate aminotransferase (AST)/alanine aminotransferase (ALT) elevation that is declared to be caused due to liver metastasis, they are allowed to be enrolled as long as \< 5 x ULN
• •Subject of childbearing potential should be willing to use effective methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study and through at least 4 months after the last dose of study drug; subject of childbearing potential is defined as has not been surgically sterilized or free from menses for \> 1 year; effective methods of birth control include: 1) use of hormonal birth control methods: pills, shots/injections, implants (placed under the skin by a health care provider), or patches (placed on the skin); 2) intrauterine devices (IUDs); 3) using 2 barrier methods (each partner must use 1 barrier method) with a spermicide; males must use the male condom (latex or other synthetic material) with spermicide; females must choose either a diaphragm with spermicide, or cervical cap with spermicide, or a sponge (spermicide is already in the contraceptive sponge); female patients of childbearing potential must have a negative urine pregnancy test no more than 7 days prior to starting study drug; 4) for male participant, they must agree and commit to use a barrier method of contraception while on treatment and for 3 months after the last dose of investigational product
• •Cohort 1: Phase 1b: patient must have HER2 + (regardless of hormonal receptor status) metastatic or locally advanced breast cancer (IBC or Non-IBC); HER2 positive status is defined as strongly positive (3+) staining score by immunohistochemistry (IHC), or gene amplification using fluorescence in situ hybridization (FISH), if performed; if IHC is equivocal (2+), please refer to current American Society of Clinical Oncology (ASCO) guidelines algorithm for evaluation of HER2; HER2 negative status, which is determined by assays using IHC require negative (0 or 1+) staining score; if IHC is equivocal (2+) staining score, please refer to current ASCO guidelines algorithm for evaluation of HER2; IBC is determined by using international consensus criteria: onset: rapid onset of breast erythema, edema and/or peau d'orange, and/or warm breast, with/without an underlying breast mass; duration: history of such findings no more than 6 months; extent erythema occupying at least 1/3 of whole breast; pathology: pathologic confirmation of invasive carcinoma
• •Cohort 1: Phase II: patient must have HER2+ (regardless of hormonal receptor status) stage III IBC or Stage IV IBC if the metastatic sites are amenable for local therapy (i.e. radiation and/ or surgery) and will have breast surgery
• •Cohort 2: Patient must have HER2-/HR+ stage III IBC or Stage IV IBC if the metastatic sites are amenable for local therapy (i.e. radiation and/ or surgery) and will have breast surgery