No, the AI and Series III families of products are not compatible, because they use different AVB protocols (AVB I and AVB II). The idea is nice, but you simply can't use a RM32AI as "stagebox" or monitor mixer.
The Series III mixers can not be cascaded and there is no possibility to expand the number of mixer channels. There is a 16 channel mixer (16R), there are the 32-channel mixers (32S, 32SX, 32SC, 32, 24, 16, 32R, 24R) and there is a 64-channel mixer (64S). If 32 input channels are not enough, you would need to get the 64S with stageboxes or a combination of rack mixers and stageboxes.