Provided that no subject experiences dose limiting toxicity (DLT) [defined as a study drug related Grade 3 or higher non-hematologic toxicity using National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) v3.0] during the first 21 days (i.e., during the first treatment cycle), the subsequent group of 3 subjects will receive the next higher liposomal annamycin dose. However, if 1 of the 3 initial subjects experiences DLT, the cohort of subjects at the initial dose level will be expanded to 6 subjects. If at least 2 of the 6 subjects experience DLT, then 3 subjects will be treated at the next lower dose. The MTD is defined as the highest dose of liposomal annamycin at which fewer than 2 (of a cohort of up to 6) subjects experience a DLT.