We propose a multiple chirp rate index modulation (MCR-IM) system based on Zadoff-Chu (ZC) sequences that overcomes the problems of low transmission rate and large-scale access in classical LoRa networks. We demonstrate the extremely low cross-correlation of MCR-IM signals across different spread factors, showing that the proposed MCR-IM system also inherits the characteristics of ZC sequences modulation. Moreover, we derive an approximate closed-form expression for the bit-error rate (BER) of the proposed MCR-IM system over Nakagami-m fading channels. Simulation results confirm the accuracy of the derived closed-form expression and demonstrate that the MCR-IM system achieves higher levels of spectral efficiency (SE) compared to existing systems. In this context, assigning multiple chirp rates to each user results in a reduction in the number of parallel channels. To mitigate this issue, we propose a peak detection based successive interference cancellation (PD-SIC) algorithm to accommodate more users. Compared to orthogonal scatter chirp spreading spectrum system that names OrthoRa, the MCR-IM system with PD-SIC algorithm achieves lower BER levels. For a similar number of collision signals, the throughput of the MCR-IM system is enhanced by 16% to 21%. Owing to these advantages, the proposed MCR-IM is well suited for large-scale, high-rate LoRa network applications.