Reduced order models (ROMs) are widely used to enable efficient simulation of mistuned bladed disks. ROMs based on projecting the system dynamics into a subspace spanned by the modes of the tuned structure work well for small amounts of mistuning. When presented with large mistuning, including changes of geometry and number of finite element mesh nodes, advanced methods such as the the pristine-rogue-interface modal expansion (PRIME) are necessary. PRIME builds a reduced model from two full cyclic symmetric analyses, one for the nominal and one for the modified type of sector. In this paper a new reduced order model suitable for large mistuning with arbitrary mesh modifications is presented. It achieves higher accuracy than PRIME, while saving approximately 25% computational effort during the reduction process, when using the same number of cyclic modes. The new method gains its efficiency by recognizing that large modifications from damage or repair are unlikely to be exactly the same for multiple blades. It works by building a partially reduced intermediate model: All nominal sectors are reduced using cyclic modes of the tuned structure. The single modified sector is kept as the full model. For this reason, the new reduction method is called Partially Reduced Intermediate System Model (PRISM) method. The accuracy of the PRISM method is demonstrated on an axial compressor blisk and an academic blisk geometry.