Compressed Air Energy Storage (CAES) technology has risen as a promising approach to effectively store renewable energy. Optimizing the efficient cascading utilization of multi-grade heat can greatly improve the efficiency and overall system performance. Particularly, the number of compressor and expander stages is a critical factor in determining the system’s performance. In this study, we focused on the Advanced Adiabatic Compressed Air Energy Storage system with Combined Heat and Power (AA-CAES -CHP). Both economic and thermodynamic models were established for the AA-CAES-CHP system. To systematically study the effects of compression and expansion stages, the influence of 3 different compressor stages and expander stages was comprehensively analyzed under 4 operating conditions. Key findings reveal that the count of compressor and expander stages have a notable impact on the exergy losses of the AA-CAES-CHP system. As for the investment cost, the proportion of investment cost for expanders decreases when the stage numbers of compressors and expanders are the same. Furthermore, both thermodynamic and economic characteristics allow us to optimize the AA-CAES-CHP system’s performance. One of our cases demonstrates that doubling the air mass flow rate results in a doubled total energy output with a relatively modest increase (41.1%–65.1%) in the total investment cost.