Achieving both a low operating temperature for photovoltaic (PV) and a high heat collection temperature for photothermal (PT) conversion in full-spectrum solar energy utilization is challenging with traditional spectrum-splitting methods. Therefore, this study focuses on the full-spectrum solar utilization and proposes a novel multi-stage concentrating and spectrum-splitting coupling approach for complementary photovoltaic-thermophotovoltaic (PV-TPV) conversion. Multi-stage thermophysical models are developed based on thermodynamic analysis, Shockley-Queisser model coupling, and external quantum efficiency model coupling, incorporating cell combinations with different bandgaps and temperature coefficients, enabling performance analysis from idealized scenarios to realistic conditions. A single-stage spectrum splitting PV-TPV system is optimized as a baseline, and the impact of multi-stage spectrum coupling on system performance is investigated. Results show that low-bandgap cells with higher temperature coefficients can achieve superior performance at lower concentration ratios compared with high-bandgap cells at higher concentration ratios. Considering the practical external quantum efficiency (EQE) model, low-bandgap cells demonstrate additional advantages, achieving a maximum system efficiency of 41.82% at C₁ = 500 and C₂ = 300. The multi-stage spectrum-splitting design allows decoupling of the spectrum and concentration ratio, effectively reducing the system concentration ratio by more than 50% while maintaining high system performance. This not only facilitates device design and practical implementation but also enhances theoretical efficiency, demonstrating significant application potential. The study provides valuable insights for the development of full-spectrum PV-TPV conversion methods.