Neratinib and Capmatinib Combination (Phase Ib/II) in Metastatic Breast Cancer and Inflammatory Breast Cancer Patients With Abnormal HER-family and c-Met Pathway Activity as Measured by the CELsignia Signaling Analysis Test

Inclusion Criteria 1. Signed Informed Consent Form (ICF) and comply with the requirements of the study protocol 2. Age ≥ 18 years. 3. ECOG performance status 0-1 4. Confirmed diagnosis of metastatic breast cancer or inflammatory breast cancer according to international consensus criteria: * Onset: Rapid onset of breast erythema, edema, and/or peau d'orange, and/or warm breast, with or 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 5. Patients who have metastatic disease which is not amenable to curative treatment with available local and systemic therapy. Patients must have received at least 1 line or up to 6 lines of therapy in the metastatic setting with at least 2 weeks washout period before the initiation of study treatment. i. Unless a contraindication to therapy exists, patients with ER+ breast cancer must have received prior endocrine therapy combined with a CDK4/6 inhibitor, patients with BRCA1 or BRCA2 mutations must have received prior PARP inhibitor, and patients with PD-L1+ triple negative breast cancer must have received prior immunotherapy. ii. Patients with HER2-positive disease must have received at least 2 regimens of anti-HER2 therapy in metastatic setting. 6. For Phase Ib, any ER, PR, and HER2 status, For Phase 2, HER2-negative per ASCO/CAP guidelines and any ER and PR status. 7. For Phase II only, Patients with measurable disease according to the Response Evaluation Criteria in Solid Tumor (RECIST, v1.1) (local or distant) and at least one metastatic lesion amenable for biopsy (core or punch) NOTE: Measurable disease: Measurable lesions are defined as those that can be accurately measured in at least one-dimension (longest diameter to be recorded) as ≥ 20mm by chest X-ray, ≥ 10mm by computed tomography (CT) scan, ≥ 10mm with calipers by clinical exam. Measurable malignant lymph nodes: To be considered pathologically enlarged and measurable, a lymph node must be ≥ 15mm in short axis when assessed by CT scan. Non-measurable disease: All other lesions (or sites of disease), including small lesions, are considered non-measurable. Bone lesions, leptomeningeal disease, ascites, pleural/pericardial effusions, lymphangitis, cutis/pulmonitis, inflammatory breast disease, and abdominal masses \[not followed by CT or magnetic resonance imaging (MRI)\] are considered non-measurable. 8. Left Ventricular Ejection Fraction ≥ 50% measured by MUGA scan or Echocardiogram. 9. Abnormal HER-family and c-Met signaling activity based on CELsignia MP Test results (for phase II patients only). 10. Participants must have adequate organ function including the following laboratory values at the screening visit. Screening must occur within 28 days prior to the first dose of study drug. Screening samples for hematology and serum chemistries must be drawn within 14 days prior to the first dose of study drug: * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L without growth factor support * Platelets (PLT) ≥ 75 x 10\^9/L * Hemoglobin (Hgb) ≥ 9 g/dL * Calculated creatinine clearance (using Cockcroft-Gault formula) ≥ 45 mL/min * Total bilirubin (TBIL) ≤ ULN (upper limit of normal) with the following exception: Patients with known Gilbert disease who have serum bilirubin level ≤ 3 x ULN may be enrolled. * Aspartate transaminase (AST) ≤ 3 x ULN, except for participants with liver metastasis, who may only be included if AST ≤ 5 x ULN * Alanine transaminase (ALT) ≤ 3 x ULN, except for participants with liver metastasis, who may only be included if ALT ≤ 5 x ULN * Alkaline phosphatase (ALP) ≤ 5.0 x ULN * Asymptomatic serum amylase ≤ grade 2. Participants with grade 1 or grade 2 serum amylase at the beginning of the study must be confirmed to have no signs and/or symptoms suggesting pancreatitis or pancreatic injury (e.g., elevated P-amylase, abnormal imaging findings of pancreas, etc.) * Serum lipase ≤ ULN 11. Willing and able to comply with scheduled visits, treatment plan and laboratory tests. Patients who are cognitively impaired who may not be able to comply with the oral study medication schedule are excluded. i) Patients with ER positive (defined at ER\>/=10%)breast cancer, must start (or continue) an aromatase inhibitor of physician choice during the study duration. In addition, pre-/peri-menopausal women with ER+ breast cancer will also require ovarian suppression therapy. 12. Non-English speaking subjects are eligible as long as a translator is available at the treating site. Exclusion Criteria: 1. Concurrent anticancer therapy within 2 weeks of initiation of study treatment; except: i. Endocrine therapy (SERM, aromatase inhibitor, fulvestrant, medical ovarian suppression therapy) ii. Palliative radiotherapy for bone metastases \< 1 week prior to study treatment 2. Unstable and symptomatic brain metastasis (Stable disease is defined as CNS radiographic study ≥ 4 weeks from completion of radiotherapy and ≥ 2 weeks from discontinuation of corticosteroids) 3. Non-hematologic adverse events from prior anticancer therapy that have not resolved to Grade ≤ 1 (CTCAE v 5.0), except for alopecia, vitiligo, pain, constipation if these symptoms existed during screening baseline. i. Grade 3 or above neuropathy induced from prior treatment, that is not resolved to grade 2 or below despite best supportive care 4. Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis 5. Acute exacerbations of underlying condition within the last 12 months (requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) 6. Patients with known HIV infection. Testing for HIV is not required for study screening: 1) CD4+ count\<350 cells/uL; or 2) had AIDS-defining opportunistic infections \< 12 months 7. Known active hepatitis B (chronic or acute) or hepatitis C infection. Testing for hepatitis is not required for study screening: i) Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HbsAg\] test and a NEGATIVE anti-HBc \[antibody to hepatitis B core antigen\] antibody test). Patient is eligible if anti-HBc is POSITIVE, but should sample for HBV DNA and referral to virologist to monitor for HBV reactivation ii) Patients with positive for hepatitis C virus (HCV) antibody and have positive polymerase chain reaction (PCR) for HCV RNA. 8. Severe infections within 4 weeks prior to study treatment, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia 9. Signs or symptoms of infection within 2 weeks prior to study treatment per treating physician and PI judgement. 10. Concurrent oral or IV antibiotics within 5 days prior to study treatment \* Patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are allowed and eligible so long as the antibiotic is not prohibited with the study medication (See Tables 8). 11. Major surgical procedure within 28 days prior to study treatment or anticipation of need for a major surgical procedure during the course of the study. 12. Presence or history of interstitial lung disease or interstitial pneumonitis, including clinically significant radiation pneumonitis (i.e., affecting activities of daily living or requiring therapeutic intervention). 13. Long QT syndrome, family history of idiopathic sudden death or congenital long QT syndrome. 14. Clinically significant, uncontrolled heart diseases. * Unstable angina within 6 months prior to screening * Myocardial infarction within 6 months prior to screening * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Uncontrolled hypertension defined by a Systolic Blood Pressure (SBP) ≥ 160 mm Hg and/or Diastolic Blood Pressure (DBP) ≥ 100 mm Hg, with or without antihypertensive medication. Initiation or adjustment of antihypertensive medication(s) is allowed prior to screening * Ventricular arrhythmias * Supraventricular and nodal arrhythmias not controlled with medication * Other cardiac arrhythmia not controlled with medication * QTcF (QT interval corrected by Fridericia's formula) ≥ 470 ms on the screening ECG (as mean of triplicate ECG) 15. Major surgery (e.g., intra-thoracic, intra-abdominal or intra-pelvic) within 4 weeks prior (2 weeks for resection of brain metastases) to starting study therapy or who have not recovered from side effects of such procedure. 16. Unable to swallow or absorb study drugs due to impairment of GI function or GI disease e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, or malabsorption syndrome 17. Participants receiving treatment with any enzyme-inducing anticonvulsant that cannot be discontinued at least 1 week before first dose of capmatinib, and for the duration of the study. 18. Other severe, acute, or chronic medical or psychotic conditions, substance abuse or laboratory abnormalities that in the opinion of the investigator may increase the risk associated with study participation, or that may interfere with the interpretation of study results. 19. Pregnant or nursing (lactating) women 20. Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception during dosing and for one month after stopping treatment. Highly effective contraception methods include: * Total abstinence (when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Male sterilization (at least 6 months prior to screening). For female subjects on the study, the vasectomized male partner should be the sole partner for that subject * Use of injected or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception. Women are considered post-menopausal and not of childbearing 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 before study entry. 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. 21. Sexually active males will not be eligible unless they use a condom during intercourse while taking drug and for 3 months after stopping treatment and should not father a child in this period. A condom is required for all sexually active male to prevent them from fathering a child AND to prevent delivery of study treatment via seminal fluid to partner. In addition, male participants must not donate sperm for the time period specified above. 22. Participants receiving treatment with the following medications that cannot be discontinued at least 1 week prior to the start of treatment with study therapy and for the duration of the study: 1. strong inducers of CYP3A 2. moderate inducer of CYP3A4 3. strong CYP3A4 inhibitor 4. concomitant use of a moderate CYP3A4 and P-gp dual inhibitor (verapamil). 5. proton pump inhibitor. Neratinib may be taken at least 2 hours before or 10 hours after an H2-receptor antagonist, and 3 hours after antacids. 6. P-gp substrates (such as digoxin, dabigatran, fexofenadine) or strong P-gp inducers (such as carbamazepine, phenytoin, rifampicin, and St. John's wort). 7. Chronic immunosuppressive therapies including systemic corticosteroids. Steroids given for physiological replacement, as anti-emetics or inhaled as well as short course of oral/topical steroids given for allergic reactions or asthma flares are allowed. 23. No prior treatment with Capmatinib, Neratinib, or other HER2 directed tyrosine kinase inhibitor (for phase II patients only).