We present a method for constructing multiphase excitations in the generally nonintegrable system of warm fluid equations describing plasma oscillations. It is based on autoresonant excitation of nonlinear electron plasma waves by phase locking with small amplitude chirped-frequency ponderomotive drives. We demonstrate the excitation of these multiphase waves by performing fully nonlinear numerical simulations of the fluid equations. We develop a simplified model based on a weakly nonlinear analytical theory by applying Whitham's averaged Lagrangian procedure. The simplified model predictions are in good agreement with the results from the warm fluid simulations. Such autoresonantly excited multiphase waves form coherent quasicrystalline structures, which can potentially be used as plasma photonic or accelerating devices. Finally, we discuss the laser parameters required for the autoresonant excitation of nonlinear waves in a plasma.