In this paper, an exhaustive general synthesis method is proposed for the extended-box topologies with dispersive couplings, which is very suitable for the realization of the monoblock dielectric resonator filters. The difficulty of introducing the diagonal cross coupling calls for the extended-box topology. When properly utilizing the inevitable dispersion effect of the negative coupling introduced by a metalized blind hole, an extra transmission zero generates. Multiple solutions can be observed by solving the polynomial equation system established based on the congruent transformation, from which the solution most suitable for realization can be selected and realized. A sixpole filter in extended-box topology with a dispersive coupling is synthesized and EM designed for validation.