I don't see 74hc596 as a purchaseable part at Digikey or Mouser. Maybe a different logic family?
"4051/4052/4053 - The CDx4HCx4051 devices are a single 8-channel multiplexer having three binary control inputs, S0, S1, and S2 and an ENABLE input. The three binary signals select 1 of 8 channels to be turned on, and connect one of the 8 inputs to the output.
The CDx4HCx4052 devices are a differential 4-channel multiplexer having two binary control inputs, S0 and S1, and an ENABLE input. The two binary input signals select 1 of 4 pairs of channels to be turned on and connect the analog inputs to the outputs.
The CDx4HCx4053 devices are a triple 2-channel multiplexer having three separate digital control inputs, S0, S1, and S2 and an ENABLE input. Each control input selects one of a pair of channels that are connected in a singlepole, double-throw configuration."
Not I2C interfaced at all, so not sure how that helps.