Dispersive coupling between vibrational modes with different frequencies is a major nonlinear dynamical effect. We show, analytically and numerically, that in $p$-doped semiconductors such coupling can be strongly enhanced. Moreover, the relative coupling strength increases with the order of the nonlinearity. The doping-induced dispersive coupling becomes much stronger than the intrinsic one already for moderately strong doping. Its dependence on the hole density is nonmonotonic, and the temperature dependence becomes nonmonotonic for higher densities. Relevant mesoscopic frequency fluctuations are briefly discussed. The theory is applied to Si resonators, where doping is often used to compensate the temperature dependence of a clock mode, whereas another low-frequency mode is used as a thermometer to enable temperature stabilization.