We assessed in mice whether broad CD8⁺ T cell responses capable of efficient recognition of multiple HIV‐1 clades could be induced using current single‐clade vaccine constructs that were or will be used in clinical trials in Europe and Africa. We found that single‐clade A, B and C vaccines applied alone induced only limited cross‐clade reactivity and that the epitope hierarchy varied according to the immunizing clade. However, combining single‐clade HIV‐1 vaccines into multi‐clade formulations resulted in multiple forms of in vivo immune interference such as original antigenic sin and antagonism, which dampened or even abrogated induction of responses to epitope variants and reduced the breadth of induced T cell responses. Simultaneous administration of individual clade‐specific vaccines into anatomically separated sites on the body alleviated antagonism and increased the number of detectable epitope responses. Although cross‐reactivity of murine CD8⁺ T cells does not directly translate to humans, the molecular interactions involved in triggering T cell responses are the same in mouse and man. Thus, these results have important ramifications for the design of both prophylactic and therapeutic vaccines against HIV‐1 and other highly variable pathogens.