In this paper, we propose a generalized block structure-preserving reduced order interconnect macromodeling method (BSPRIM). Our approach extends structure-preserving model order reduction (MOR) method SPRIM [4] into more general block forms. We first show how SPRIM-like structure-preserving MORmethod can be extended to deal with admittance RLC circuit matrices and show the 2q moments are still matched and symmetry is preserved. We then show that 2q moment matching can't be achieved when the RLC circuits are driven by both current and voltage sources. The new approach also improves SPRIM by introducing the re-orthonormalization process on the partitioned projection matrix. Then we present our BSPRIM method to deal with more circuit partitions and show the resulting general block structure preserving MOR for linear dynamic circuits formulated in impedance and admittance forms. The reduced models by the proposed BSPRIM will still match the 2q moments and preserve the circuit structure properties like symmetry as SPRIM does. Experimental results demonstrate effectiveness of the proposed methods and it outperforms SPRIM in terms of accuracy with more partitions.