This randomized, open-label study will compare immediate salvage therapy using combination antiretroviral therapy plus T-20 (enfuvirtide, Fuzeon) with a 16-week structured treatment interruption (STI) followed by combination therapy plus T-20. The study will examine whether STI helps improve the chances of successful treatment in people who have HIV that is resistant to multiple drugs. Virological response will be measured at weeks 16, 32, and 48. All participants will receive T-20 either immediately or after 16 weeks; T-20 is administered by subcutaneous (under the skin) injection twice daily. The other drugs in each subject's regimen should be the strongest antiretroviral combination available.