Cohorts of 3-6 patients receive escalating doses of cisplatin, alvocidib, and irinotecan hydrochloride until the maximum tolerated dose (MTD) of each is determined. The MTD is defined as the dose preceding that at which at least 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. Once the MTD is determined, 12 additional patients are treated at the recommended phase II dose.