We present a semiclassical theory of an optically pumped quantum dot phonon laser, based on a system of N quantum dots coupled to a high-Q acoustic phonon cavity. Based on a theory developed earlier [J. Kabuss, A. Carmele, and A. Knorr, Phys. Rev. B 88, 064305 (2013)], that was limited to the single emitter limit, a set of phonon laser equations is generalized to the many emitter regime and solved analytically. Similar to the optical laser it is possible to overcome the adverse effect of a phonon cavity loss with respect to entering the phonon laser regime by the number of quantum dots, that are coupled to the phonon resonator mode. Especially in the case of the proposed quantum dot phonon laser, which exhibits self-quenching, a shift of the laser threshold to lower pump powers and an inhibition of the self-quenching can be essential for entering the phonon lasing regime in the first place.