This paper presents an analytical method for the synthesis of a low-pass prototype filter constituted by cascaded n-tuplets including resonant and non-resonant nodes. The method extends the features of previous published solutions, limited to resonant nodes only or that allow the inclusion of non-resonant nodes but in rigid configurations. The method begins with extracted-pole synthesis, arbitrarily defining the transmission zeros. Then, a filter topology transformation is applied by grouped node blocks to obtain the desired topology, with each n-tuplet characterized by the assigned transmission zeros. The procedure overcomes the ad-hoc techniques currently available in the literature. Moreover, the novel filter transformation presented here (from extracted-pole to cross-coupled topology) provides an additional degree of freedom for filter synthesis, which can be further exploited by filter designers. Several examples are presented to validate the novel synthesis procedure.