The HNC (hypernetted-chain) theory for two-body correlation in fluids is generalized so that up to M-body (M > 2) correlation functions can be obtained self-consistently. Our approach is based on the M-body density functional theory and a generalized Percus idea where maximally M-1 particles are held fixed in space, leading to M-1 HNC equations for the correlation functions. These are supplemented with M-1 Ornstein-Zernike relations to give a closed set of equations. Due to the rather complicated structure of the coupled integral equations, we explicitly present the equations for the case M=3, which are compared with the HNC2 equations by Verlet. The M=3 theory is numerically solved for the case of a one-dimensional liquid.