Infection with HIV is characterized by very diverse disease–progression patterns across patients, associated with a wide variation in viral set–points. Progression is a multifactorial process, but an important role has been attributed to the HIV–specific T–cell response. To explore the conditions under which different set–points may be explained by differences in initial CD4 and CD8 T–cell responses and virus inoculum, we have formulated a model assuming that HIV–specific CD4 cells are both targets for infection and mediators of a monoclonal or polyclonal immune response. Clones differ in functional avidity for HIV epitopes. Importantly, in contrast to previous models, in this model we obtained coexistence of multiple clones at steady–state viral set–point, as seen in HIV infection. We found that, for certain parameter conditions, multiple steady states are possible: with few initial CD4 helper cells and high virus inoculum, no immune response is established and target–cell–limited infection follows, with associated high viral load; when CD4 clones are initially large and virus inoculum is low, infection can be controlled by several clones. The conditions for the dependence of viral set–point on initial inoculum and CD4 T–helper clone availability are investigated in terms of the effector mechanism of the clones involved.