The equations of motion of multiple M0-brane (multiple M-wave or mM0) systems in an arbitrary D ¼ 11 supergravity superspace, which generalize the matrix model equations for the case of interaction with a generic 11-dimensional supergravity background, are obtained in the frame of the superembedding approach. We also derive the Bogomol'nyi-Prasad-Sommerfeld (BPS) equations for supersymmetric bosonic solutions of these mM0 equations and show that the set of 1=2 BPS solutions contain a fuzzy sphere modeling M2 brane as well as that the Nahm equation appears as a particular case of the 1=4 BPS equations.