Disordered proteins frequently serve as interaction hubs involving a constrained variety of partners. Complexes with different partners frequently exhibit distinct binding modes, involving regions that remain disordered in the bound state. While the conformational properties of disordered proteins are well-characterized in their free states, less is known about the molecular mechanisms by which specificity can be achieved not with one but with multiple partners. Using the energy landscape theory concept of protein frustration, we demonstrate that complexes of disordered proteins exhibit a high degree of local frustration, especically at the binding interface. These suboptimal interactions lead to the possibility of multiple bound substates, each displaying distinct frustration patterns, which are differently populated in complexes with different partners. These results explain how specificity of disordered proteins can be achieved without a single common bound conformation and how the confliict between different interactions can be used to control the binding to multiple partners.