PTX-200, Paclitaxel, Doxorubicin Hydrochloride, and Cyclophosphamide in Treating Patients With Stage IIB-IV Breast Cancer

Inclusion Criteria: * Phase I and expansion cohort: Patients must have histologically or cytologically confirmed adenocarcinoma of the breast associated with clinical stage: IV (see American Joint Committee on Cancer \[AJCC\] staging criteria, 7th edition) or stage IIB-IIIC (expansion cohort only) * Phase II: Patients must have histologically or cytologically confirmed adenocarcinoma of the breast associated with the following clinical stage: IIB, IIIA, IIIB, or IIIC (see AJCC staging criteria, 7th edition); the tumor must be human epidermal growth factor receptor 2 (Her2)/neu negative (by DAKO HercepTest, fluorescence based in situ hybridization \[FISH\], or other approved assay) * Phase I and expansion cohort: Up to two prior non-taxane chemotherapy regimens for metastatic disease are permitted for patients enrolled on the phase I portion of the trial; patients with HER2/neu positive breast cancer are not eligible; patients treated with prior anthracycline therapy as neoadjuvant, adjuvant, or metastatic therapy are not eligible unless the following conditions are met: (a) prior cumulative doxorubicin dose is =\< 240 mg/m\^2 (or epirubicin dose is =\< 400 mg/m\^2), and (b) left ventricular ejection fraction (LVEF) obtained at baseline is at least 50% (or \>= 5% above lower institutional limits of normal whichever is higher); patients with estrogen receptor (ER)-positive disease are required to have relapse or progression on at least one line of endocrine therapy * Phase II: No prior chemotherapy, irradiation, or definitive therapeutic surgery (e.g., mastectomy or lumpectomy or axillary dissection) for this malignancy; patients who have had a prior sentinel lymph node biopsy for this malignancy are eligible * Patients who received tamoxifen or another selective estrogen receptor modulator (SERM) for prevention or treatment of breast cancer or for other indications (e.g., osteoporosis, prior ductal carcinoma in situ \[DCIS\]), or who receive aromatase inhibitors for prevention or treatment of breast cancer, are eligible; patients who are hormone-receptor positive and who have received other hormonal agents for the treatment of breast cancer (e.g., Fulvestrant) are also eligible; tamoxifen therapy or other hormonal agents should be discontinued at least 1 week before the patient is enrolled on this study * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Leukocytes \>= 3,000/uL * Absolute neutrophil count =\< 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x institutional upper limit of normal * Left ventricular ejection fraction (LVEF) within normal institutional limits * Creatinine within normal institutional limits * LVEF at or above institutional lower limits of normal (\>= 50%), or at least 5% above lower limits of normal if prior anthracycline exposure (by echocardiogram or nuclear scan within 12 weeks of registration) * Electrocardiogram (ECG) corrected QT (QTC) \< 450 msec * Serum calcium within normal institutional limits * Serum phosphorus within normal institutional limits * Fasting glucose within normal limits * Patients must be disease-free of prior invasive malignancies for \>= 2 years with the exception of curatively-treated basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the cervix (for phase II only); patients with the following prior or concurrent diagnoses are eligible: lobular carcinoma in situ, contralateral ductal carcinoma in situ, or contralateral invasive ductal and/or lobular cancer (and no prior adjuvant chemotherapy for previous breast malignancy) * Women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not be receiving any other investigational agents during protocol therapy, or up to 30 days prior to beginning protocol therapy; there should be a least a 1-week interval between last dose of endocrine therapy and protocol therapy, and at least 3 weeks for the last dose of biologic therapy (eg, bevacizumab) or cytotoxic therapy (or 2 weeks for capecitabine or weekly paclitaxel, 6 weeks for mitomycin-C and nitrosoureas), and adequately recovered from adverse effects from prior therapy to meet all other eligibility criteria * History of allergic reactions attributed to compounds of similar chemical or biologic composition to PTX-200 or other agents used in the study (e.g., imidazoles, quinolones) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, diabetes mellitus requiring therapy (insulin or oral hypoglycemic agents), congenital prolonged QT syndrome, requirement for a drug known to prolong the QT interval, a history of QT prolongation, a screening QTc \>= 450 msec, hypertriglyceridemia requiring therapy, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, 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 PTX-200; these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients receiving combination antiretroviral therapy are excluded from the study