A variety of time-integration schemes have been suggested to improve the efficiency of a transient analysis for multiply-connected object. It is straightforward to implement the explicit schemes . However, those often struggle to satisfy the required kinematic constraint accurately and are subject to severe restriction on the critical time step size due to the stability condition. Implicit scheme, in contrast, will enable a stable constraint enforcement even for large time step size. But those typically require expensive matrix factorization or iterative solution and thus may suffer from convergence difficulty. In this abstract, an efficient approach which accomodates large time step size for multiply-connected object will be proposed by combining the PartStiff strategy onto an implicit–explicit time-integration scheme . The PartStiff approach simplifies Lagrange-multiplier-based constraints through a coupling projector, and thereby allows each substructure to be treated independently. In addition, an explicit approximation with the stiffness decomposition will be introduced within an implicit-scheme framework to simultaneously achieve stability and computational efficiency for the unassembled matrices. The proposed framework will be further discussed in comparison with existing domain-decomposition and time-integration scheme, and a non-matching coupling strategy be outlined to facilitate broader applicability to general multibody dynamic object.