Hello Thomas,
You could probably make the external analog MUX expansion work OK. However, a completely different method might also be given consideration. This is to use a separate low pin count, low cost, 8-bit MCU to provide the ADC expansion channels. This would probably utilise the SPI to communicate with the main MCU - you would need to devise a suitable protocol.
Whether to use interrupts or polling for the ADC would depend to some extent on other tasks performed by the main MCU, and the sampling frequency of the ADC measurements required for each channel. If you were to use a secondary MCU, it would probably not require interrupt use since it would be dedicated to ADC operation.
Regards,
Mac