To assess the influence of mistuning on the vibration amplitudes of turbo-machinery rotors, reduced order models (ROMs) are widely used. A variety of methods are available for single-stage configurations and mostly aero-elastic effects can be taken into account. More recent research focusses on extending these methods to include multiple stages. However, due to the significantly increased computational effort of the aeroelastic simulations when adding more stages to the models, these ROMs are rarely applied with the inclusion of multistage aeroelastic effects. It is therefore desirable to develop reduction methods which minimize the number of these simulations to reduce the computational cost and thereby enable analyses of rotors with multiple stages including aeroelastic effects. In this paper, a cyclic Craig-Bampton reduction method with an a priori interface reduction for multistage rotors is extended with an additional a posteriori interface reduction to reduce the number of aeroelastic simulations necessary for a given accuracy level of the ROM. The interface degrees of freedom between stages are reduced using a modified version of Characteristic Constraint Modes, to yield a more efficient representation of their displacements while retaining their monoharmonic nature. The method is applied to a two-stage axial compressor with full aeroelastic coupling between the stages and its reduced computational effort is demonstrated. Additionally, two sorting methods for the degrees of freedom (DOFs) of the ROM are compared.