The kinase-inducible domain interacting (KIX) domain of the CREB binding protein (CBP) is capable of simultaneously binding two intrinsically disordered transcription factors, such as the mixed-lineage leukemia (MLL) and c-Myb peptides, at isolated interaction sites. In vitro, the affinity for binding c-Myb is approximately doubled when KIX is in complex with MLL, which suggests a positive cooperative binding mechanism, and the affinity for MLL is also slightly increased when KIX is first bound by c-Myb. Expanding the scope of recent NMR and computational studies, we explore the allosteric mechanism at a detailed molecular level that directly connects the microscopic structural dynamics to the macroscopic shift in binding affinities. To this end, we have performed molecular dynamics simulations of free KIX, KIX-c-Myb, MLL-KIX, and MLL-KIX-c-Myb using a topology-based Gō-like model. Our results capture an increase in affinity for the peptide in the allosteric site when KIX is prebound by a complementary effector and both peptides follow an effector-independent folding-and-binding mechanism. More importantly, we discover that MLL binding lowers the entropic cost for c-Myb binding, and vice versa, by stabilizing the L₁₂-G₂ loop and the C-terminal region of the α₃ helix on KIX. This work demonstrates the importance of entropy in allosteric signaling between promiscuous molecular recognition sites and can inform the rational design of small molecule stabilizers to target important regions of conformationally dynamic proteins.