COHORT I (SAFETY ANALYSIS, closed to accrual): Patients receive cixutumumab intravenously (IV) over 1 hour on days 1, 8, and 15. Patients also receive capecitabine orally (PO) twice daily (BID) on days 1-14 and lapatinib ditosylate PO once daily (QD) on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.