The Multi-Mode Mean Field Annealing (MM-MFA) approach to combinatorial optimization is introduced as a tool to design recursive (IIR) digital filters with discrete coefficients. As an application example demonstrating the potential of the method we consider the design of structurally passive IIR digital filters realized as the sum of two allpass functions. The new design technique facilitates the solution of non-trivial filter design problems such as satisfying a general frequency specification by solving a combinatorial optimization problem over discrete coefficients and a max-norm cost. The final solution is not guaranteed to be a globally optimal solution but the convergence time is short enough to allow interactive design even for large problems.