This phase I trial studies how well chemokine modulation therapy and standard chemotherapy given before surgery work in treating patients with early stage triple negative breast cancer. Chemokine modulation therapy, including celecoxib, recombinant interferon alfa-2b, and rintatolimod, may stimulate the immune system and stop tumor cells from growing. Drugs used in standard chemotherapy, such as paclitaxel, doxorubicin, and cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving chemokine modulation therapy together with standard chemotherapy may work better than giving either therapy alone in treating patients with triple negative breast cancer.

PRIMARY OBJECTIVE:

I. To examine the safety and tolerability profile of the combination of rintatolimod celecoxib +/- interferon alpha-2b, when given as CKM along with chemotherapy in the neoadjuvant setting in early stage triple negative breast cancer.

II To identify the appropriate dose level of CKM and paclitaxel for future clinical exploration.

SECONDARY OBJECTIVES:

II. • Evaluate the effect of neoadjuvant CKM + paclitaxel on pathological response and breast MRI response in early stage triple negative breast cancer patients.

III. • Evaluate the overall and recurrence-free survival in early stage triple negative breast cancer patients that received neoadjuvant CKM + paclitaxel.

EXPLORATORY OBJECTIVES:

I• To evaluate longitudinal changes of blood biomarkers such as peripheral T-cell subsets, myeloid derived suppressor cells (MDSC), expression of chemokine and other immune genes, circulating immune mediators and correlate them with the clinical course post surgery.

II• Comparison of response assessment criteria for a prospective analysis using RECIST 1.1. and irRECIST

• Evaluate changes in the intratumoral levels of biomarkers, such as, peripheral T-cell subsets, myeloid derived suppressor cells (MDSC), chemokines, and immune-regulatory factors (pre- vs post-CKM + paclitaxel treatment).

OUTLINE: This is a phase Ib, dose-escalation study of recombinant interferon alfa-2b.

Patients receive celecoxib orally (PO) twice daily (BID), recombinant interferon alfa-2b intravenously (IV) over 20 minutes (omitted in lowest dose level), and rintatolimod IV on days 1-3 of weeks 1-3, as well as paclitaxel IV over 1 hour once weekly on day 1. Treatment continues for a total of 12 weeks in the absence of disease progression or unacceptable toxicity. 1-3 weeks after last dose of paclitaxel, patients receive doxorubicin IV over 10 minutes and cyclophosphamide IV over 30 minutes. Treatment repeats every 2 weeks for 4 cycles in the absence of disease progression or unacceptable toxicity.

. After completion of study treatment, patients are followed up at 2 weeks.

Inclusion Criteria:

• Have pathologically confirmed diagnosis of resectable triple negative breast cancer (ASCO/CAP guidelines will be used to define triple negative breast cancer)
• Must have measurable disease. Multi-centric disease is allowed. If patient has another lesion which is biopsied with ER/PR positive it will be Physician discretion for this eligibility criteria.
• Prior therapy: No prior cytotoxic regimens are allowed for this malignancy. Participants may not have had prior chemotherapy, other targeted anticancer therapies, or prior radiation therapy to the ipsilateral breast for this malignancy. Prior bis-phosphonate therapy is allowed
• Patient eligible for surgery as determined by patient's surgeon
• Patient must have a lesion that amendable to biopsy, unless inaccessible and with PI approval
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of =< 2
• Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Ability to swallow and retain oral medication
• Ability to undergo magnetic resonance imaging (MRI)
• Platelets >= 100,000/uL
• Hemoglobin >= 9 g/dL
• Absolute neutrophil count (ANC) >= 1500/uL
• Total bilirubin =< institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) and ALT (serum glutamate pyruvate transaminase [SGPT]) =< 1.5 X institutional upper limit of normal (ULN)
• Creatinine < ULN OR creatinine clearance >= 50 mL/min per Cockcroft-Gault equation for patients with creatinine levels greater than ULN
• Left ventricular ejection fraction (LVEF) >= 55%; if LVEF is < 55% and patient is otherwise study-eligible, the principal investigator (PI) will discuss with cardiologist if patient is eligible to receive doxorubicin and participate in study
• Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure
• Participants on this study will be counseled on and are willing to use adequate contraceptive methods

Exclusion Criteria:

• Patients currently treated with systemic immunosuppressive agents, including steroids, are ineligible until 3 weeks after removal from immunosuppressive treatment

• Patients with active autoimmune disease, requiring ongoing immunosuppressive therapy or history of transplantation

• Diagnosis of invasive carcinoma within the last 3 years

• Inflammatory breast cancer will be excluded from the study

• Participants who have metallic surgical implants that are not compatible with an MRI machine are not eligible

• Pregnant or nursing female participants

• Unwilling or unable to follow protocol requirements

• Patients with known serious mood disorders. (Major depression is an exclusion. Other stable mood disorders on stable therapy for > 6 months may be allowed after consultation with PI)

• Cardiac risk factors including:

  • Patients experiencing cardiac event(s) (acute coronary syndrome, myocardial infarction, or ischemia) within 3 months of signing consent
  • Patients with a New York Heart Association classification of III or IV

• History of upper gastrointestinal ulceration, upper gastrointestinal bleeding, or upper gastrointestinal perforation within the past 3 years

• Prior allergic reaction or hypersensitivity to nonsteroidal anti-inflammatory drugs (NSAIDs) or any drugs administered on protocol

• Any history of allergy to sulfonamides

• Any history of autoimmune hepatitis

• Grade 1 or higher neuropathy

• Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug