Capecitabine and Lapatinib Ditosylate With or Without Cixutumumab in Treating Patients With Previously Treated HER2-Positive Stage IIIB-IV Breast Cancer

Exclusion Criteria

• •Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:
• •* Pregnant women
• •* Nursing women
• •* Men or women of childbearing potential who are unwilling to employ adequate contraception (as determined by the treating physician)
• •Stage III or IV invasive cancer, other than breast cancer, in =\< 5 years prior to registration
• •Actively being treated for other malignancy, excepting non-melanotic skin cancer or carcinoma-in-situ of the cervix; if there is a history of prior malignancy, patient must not be receiving other specific treatment for their cancer
• •New York Heart Association class III or IV cardiovascular disease
• •Current, active hepatic or biliary disease except Gilbert's syndrome or asymptomatic gallstones
• •Evidence of active brain metastasis including leptomeningeal involvement; central nervous system (CNS) metastasis controlled by prior surgery and/or radiotherapy is allowed
• •* NOTE: To be considered controlled, there must be at least 2 months of no symptoms or evidence of progression prior to study entry and corticosteroid therapy must have been discontinued
• •Major surgery, chemotherapy, or immunologic therapy =\< 4 weeks prior to registration
• •Radiotherapy =\< 4 weeks prior to registration, except if to a non-target lesion only; prior radiation to a target lesion is permitted only if there has been clear progression of the lesion since radiation was completed; if patient receives single dose radiation for palliation or radiation to non-target lesion, they may immediately proceed to registration without waiting; acute adverse events from radiation must have resolved to =\< Common Terminology Criteria for Adverse Events (CTCAE) version (v) 3.0 grade 1
• •Prior treatment with any therapy targeting IGF-I, IGF-II or its receptors (either monoclonal antibody or tyrosine kinase inhibitor), including but not limited to any of the following (which would have been received on a previous clinical trial):
• •* IMC-A12 (cixutumumab)
• •* CP-751,871 (figitumumab)
• •* AMG-479
• •* INSM-18
• •* MK0646 (h7C10)
• •* SCH717454 (19D12, robatumumab)
• •* R1507
• •* OSI-906
• •* BMS-754807
• •* PPP
• •* NVP-AEW541
• •* AVE-1642
• •* MEDI-573
• •Prior therapy with any therapy targeting HER1 (EGFR) and/or HER2 (either monoclonal antibody or tyrosine kinase) other than trastuzumab, including but not limited to any of the following:
• •* Lapatinib (Tykerb)
• •* Gefitinib (Iressa)
• •* Erlotinib (Tarceva)
• •* Cetuximab (Erbitux)
• •* Panitumumab (Vectibix)
• •Currently receiving treatment with any agents that are contraindicated by study therapies:
• •* IMC-A12 - none identified to date
• •* Lapatinib - CYP3A4 inhibitors and inducers, including grapefruit and grapefruit juice
• •* Capecitabine - warfarin (Coumadin), cimetidine (Tagamet), allopurinol (Lopurin), sorivudine (Usevir) or brivudine (Brivex), ketoconazole (Nizoral), itraconazole (Sporanox), ritonavir (Norvir), amprenavir (Agenerase) or indinavir (Crixivan)
• •Uncontrolled intercurrent illness including, but not limited to:
• •* Poorly controlled diabetes
• •* Ongoing or active infection
• •* Symptomatic congestive heart failure
• •* Unstable angina pectoris
• •* Cardiac arrhythmia
• •* Psychiatric illness/social situations that would limit compliance with study requirements
• •Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of the safety of the prescribed regimens
• •Currently receiving treatment in a different clinical study in which investigational procedures are performed or investigational therapies are administered
• •Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive with an acquired immune deficiency syndrome (AIDS)-defining illness; HIV positive patients with cluster of differentiation (CD) 4 count within institutional normal range and no history of an AIDS-defining illness are eligible; however, some antiviral/antiretroviral medications which have CYP3A4 interactions are prohibited on this study