Topotecan, ifosfamide, and carboplatin will be given for the first three days of each course. Ifosfamide and carboplatin will be given into a vein for one hour each day along with the drug mesna. Mesna is not an anti-cancer drug but a drug to help protect the bladder from the potential damaging effects of ifosfamide. After the first dose of mesna, participants will receive 3 more doses (one every three hours) over 15-30 minutes . Topotecan is given directly into a vein for one-half hour beginning one hour after treatment with ifosfamide, carboplatin, and the first dose of mesna is completed. Participants who are 22 years or older will only receive Day 1 and 2 of carboplatin.