The initial 15-20 patients (in the solid tumor or multiple myeloma or lymphoma stratum) receive suberoylanilide hydroxamic acid (SAHA) IV over 2 hours on day 1 of week 0 and then orally once or twice daily beginning on day 1 of week 1. All remaining patients receive oral SAHA once or twice daily beginning on day 1 of week 1. Courses repeat every 4 weeks for up to 1 year in the absence of disease progression or unacceptable toxicity.