Yes, you can have both MICs. But, the level of each type of MIC you build is restricted based on your government--Type 4 gets better regional MICs at the expense of high-level factional MICs, and vice versa for Type 1. Yes, you can build a Type 4, build to the top regional MIC, then raze the Type 4, build a Type 1, and max out your factional MIC, but the number of provinces where this is actually beneficial (high-level regional and factional troops available) is low.

Romani factional MICs can only be built in Capua, Roma, Arretium, Ariminum, and Arpi (and Segesta after the patch) until after the Marian reforms.