We use weighted characteristic polynomials to compute Tutte polynomials of generalized parallel connections in the case in which the simplification of the maximal common restriction of the two constituent matroids is a modular flat of the simplifications
of both matroids. In particular, this includes cycle matroids of graphs that are identified along complete subgraphs. We also develop formulas for Tutte polynomials of the k-sums that are obtained from such generalized parallel connections.
Bonin, J.; de Mier, A. Tutte polynomials of generalized parallel connections. "Advances in applied mathematics", 2004, vol. 32, núm. 1-2, p. 31-43.