The well known aggressive space mapping technique has been widely used for the design of complex microwave circuits. Many extensions of ASM have been developed in recent times. These methods improve ASM either at the cost of increasing the number of fine model evaluations, or at the cost of decreasing the accuracy of the fine model. In this work, we present a new extension of ASM, the multimodel ASM (MASM) that uses several fine models of increasing accuracy. Following an iterative procedure, it gradually maps the coarse and the finest model, thus reducing the risk of divergence, and improving the overall efficiency and robustness of the design process, without reducing the accuracy of the results. The new MASM has been tested with the design of a six-pole H plane coupled cavities filter with rounded corners in the coupling windows due to die casting fabrication.