Hi,
currently, as you know that both the quadTimer and quadratute decoder modules can decode the Encoder signals,each quadTimer module can decoder ONE encoder signals.
The MC56F84789 has 2 quadTimer modules and ONE quadratute decoder module, so it can connect with 3 encoder, the quadratute decoder has index and home signal besides the PhaseA/B signals.
This is link of MC56F84789:
https://www.nxp.com/products/processors-and-microcontrollers/additional-mpu-mcus-architectures/digit...
I think you can consider i.mxrt family for example i.mxrt1060, it has 4 quadTimer modules and 4 quadratute decoder module, in other words, it can interface with 8 encoder(incremental encoder with index and home signals).
https://www.nxp.com/products/processors-and-microcontrollers/arm-microcontrollers/i-mx-rt-crossover-...
You can consider also Kinetis KV family, for example KV56, it has 4 FTM module, the FTM1/FTM2 module support quadrature decoder, and it has one Quadrature Encoder/Decoder (ENC), so it can interface with 3 encoders.
https://www.nxp.com/products/processors-and-microcontrollers/arm-microcontrollers/general-purpose-mc...
If your application is auto, you can consider S32K or MPC56xx.
Hope it can help you
BR
XiangJun Rong