Multiplexer to switch between many sets of 8 channels
I would suggest multiple 8-input ADCs instead, such as MCP3208, which is an 8-input ADC with SPI interface. Layout would be simpler: connector to chip, then parallel SCK/MOSI/MISO 16 chips in parallel, and 2 shift registers to create the 16 chip selects.  Only need 4 pins from microprocessor to control them all.

Will keep your incoming signals cleaner too, not all overlapping each other trying to feed into a single chip. Just a short trace from the connector to the MCP3208.