All participants will receive pegylated liposomal doxorubicin through a vein over about 2 hours. The drug will be given once every 21 days (3 weeks or 1 cycle). Gemcitabine will be given through a vein over 30 minutes on Days 1 and 8 every 21 days. Patients will only receive the combination of both drugs on Day 1; on that day pegylated liposomal doxorubicin will be given before the dose of gemcitabine. Bortezomib will be given by vein on Days 1, 4, 8 and 11 of every 21 days, except for the first group of patients who will receive it on days 1 and 8 only. Participants whose tumors are responding to treatment may continue treatment if their doctor approves for as long as they respond, as long as there are no serious side effects.