We predict the emergence of novel collective electronic excitations in warm dense matter with an inhomogeneous electronic structure based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. Most importantly, these modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.