 This study will evaluate the safety and tolerability of R1507 in combination with 12 distinct standard chemotherapy drug regimens and an additional R1507 monotherapy arm in patients with advanced malignant neoplasms.The 12 regimens will be tested in parallel. There are 3 subsets of patients who are eligible for the study: untreated, treated and requiring further treatment, or treated and failed and for whom adding R1507 represents a suitable treatment for their disease. All regimens will first test doses of R1507 which are less than the maximally administered dose, and if tolerated, the dose will be escalated in subsequent patients. The anticipated time on study treatment is until disease progression, and the target sample size is 100-500 individuals. 