This paper deals with the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. Departing from a four-waves model for the speeds of propagation arising at each vertex of the computational structured mesh, we present a general strategy for constructing genuinely multidimensional Riemann solvers, that can be applied for solving systems including source and coupling terms. In particular, a simple version of a well-balanced 2d HLL scheme is presented, which is later taken as a basis to build a general class of incomplete Riemann solvers, the so-called Approximate Viscosity Matrix (AVM) schemes. The great advantage of the AVM strategy is the possibility to control the amount of numerical diffusion considered for each hyperbolic system at an affordable computational cost. The presented numerical schemes are shown to be linearly -stable for a CFL number up to unity. Our schemes can be used as building blocks for constructing high-order schemes. In this work, a second-order scheme is constructed by using a predictor-corrector MUSCL-Hancock procedure. To test the performances of the proposed schemes, a number of challenging numerical experiments in one-layer and two-layer shallow water systems have been run. The presence of the bottom topography and the coupling terms represent an additional difficulty, that has been solved by reformulating the problem within the path-conservative framework. Finally, the 2d schemes have been shown to be more efficient than their projected 1d×1d counterparts.