Ibalizumab is a monoclonal antibody that works by blocking HIV entry into the immune system cells (CD4+ or T-cells) the virus typically infects. Ibalizumab is intended for use in combination with other anti-HIV drugs in people with multi-drug resistant HIV and limited treatment options. This study will collect further information on the safety and tolerability of intravenously administered (IV) ibalizumab combined with an optimized background regimen for treating multi-drug resistant HIV-1 infection, and will provide continuing access to ibalizumab for patients completing a prior ibalizumab clinical trial.