The purpose of this research study is to determine the safety and maximum tolerated dose of PCI-24781 that can be given safely with doxorubicin (phase I) and the safety and efficacy of PCI-24781 when used in combination with doxorubicin (phase II) in patients with advanced sarcomas. The study drug, PCI-24781, is believed to regulate genes involved in tumor cell growth. The other study drug, doxorubicin, is considered a standard chemotherapeutic treatment for advanced sarcoma patients. We hypothesize that combining PCI-24781 with doxorubicin can overcome chemoresistance to doxorubicin.

• In the phase I portion of the study, since we are looking for the highest dose of PCI-24781 that can be administered safely without severe or unmanageable side effects in participants that have advanced sarcoma, not everyone who participates in this research study will receive the same dose of PCI-24871.
• Each treatment cycle is 3 weeks (21 days). Participants will take capsules of PCI-24871 for five consecutive days starting on Day 1 of each 3 week cycle. On Day 4 of each cycle, participants will come to the clinic to receive doxorubicin intravenously.
• At specific time intervals, participants will return to the clinic for the following tests and procedures: physical examination, vital signs, blood tests, urine test, EKG, assessment of the tumor by CT scan, and an ECHO or MUGA.
• Participants may remain on the study for a maximum of 6 cycles (about 4-5 months). After the last cycle, as long as the participant is showing benefit, they may elect to continue taking PCI-24781 alone, in which case they will continue in this research study until there is evidence of their tumor growing.

Inclusion Criteria:

• Participants must have histologically confirmed metastatic or unresectable sarcoma
• All participants must have received no more than a lifetime cumulative maximum dose of 300 mg/m2 or less of prior doxorubicin and no other anthracycline therapy.
• Participants must have measurable disease, defined as at least one unirradiated lesion that can be accurately measured in at least one dimension as 20mm or greater with conventional techniques or as 10mm or greater with spiral CT scan.
• ECOG performance status of 2 or less
• Ability to swallow oral capsules without difficulty
• Participants must have normal organ and marrow function as outlined in the protocol.
• Women of childbearing potential must have a negative serum/urine pregnancy test within 7 days prior to receiving the first dose of PCI-24781.
• An ECHO or MUGA demonstrating EF > 50% is required within 4 weeks prior to study drug administration.
• 18 years of age or older

Exclusion Criteria:

• Participants who have had immunotherapy, chemotherapy, experimental therapy or radiotherapy within 4 weeks before first day of study drug dosing or those who have not recovered to grade 1 or baseline from adverse events due to agents administered more than 4 weeks earlier.
• Participants who have previously received > 300 mg/m2 cumulative lifetime dose of doxorubicin, or who have received any other anthracycline chemotherapy.
• Major surgery within 4 weeks before first day of study drug dosing
• Participants with known central nervous system/brain metastases
• Participants receiving chronic corticosteroids > 20 mg prednisone equivalent per day for > 7 consecutive days (Topical, inhaled or nasal corticosteroids are permitted).
• Participants with any documented malabsorption syndromes or other conditions that may impair the absorption of PCI-24781 capsules.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Participants requiring concurrent therapeutic anticoagulation or have received therapeutic anticoagulation within 2 weeks of the first day of dosing.
• Risk factors for Torsades de Pointes, or use, within 4 weeks of starting study drug administration, of medications known to prolong QTc interval or that may be associated with Torsades de Pointes.
• QTc prolongation or other significant ECG abnormalities defined as 2nd degree AV block type II, 3rd degree AV block, or bradycardia.
• History of myocardial infarction, acute coronary syndromes, coronary angioplasty and/or coronary artery stenting within the past 6 months.
• For patients with history of major coronary artery disease in the judgement of the responsible physician, a cardiac stress test that demonstrates clinically significant abnormalities when performed within 28 days of first dose of study drug
• Pregnant or breastfeeding women
• Women of childbearing potential, or sexually active men unwilling to use adequate contraceptive protection during the course of the study
• HIV-positive individuals
• Other medical or psychiatric illness or organ dysfunction that, in the opinion of the investigator, would either compromise the patient's safety or interfere with the evaluation of the safety of PCI-24781