In this paper an approach to the synthesis of coupling matrices for microwave filters is presented. The approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc. that is best suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently introduced 'extended box' (EB) coupling matrix configuration is taken. The EB represents a class of filter configuration featuring a number of important advantages, one of which is the existence of multiple coupling matrix solutions for each prototype filtering function, e.g. 16 for 8th degree cases. This case is taken as an example to demonstrate the use of the synthesis method yielding one solution suitable for dual-mode realization and one where some couplings are small enough to neglect.