No, cascading is no option for Series III mixers.
Basically Series III has several 32 channel / 16 aux mixer models, the 64 / 32 mixer and the 16 / 6 rack mixer. Whatever you might want to combine, it will stay in these "frames" (32/16, 64/32, 16/6). Adding NSB stageboxes does not increase the number of inputs and outputs, but you could rote flex mix outputs 13-16 to a NSB stagebox for physical outputs.
There is the option to use mixers in "Stand Alone Mode", which means that two mixers, connected via AVB, share their inputs, but act totally separate. In your example 32R / 24R this would be 32 analog input channels (the samew for both rack mixers) and 16 + 12 = 28 flex mix outputs.
Everything beyond 32 input channels can only be handled by a SL 64S, which also has 32 flex mix outputs.