CMP model for multnomial probit with varying choice set

Hello,

I am looking to build a multinomial probit with a varying choice set for each individual via CMP. The idea is to later add other choice dimensions for building a joint model and hence I am looking for a workaround using CMP.

I understand that the "asmprobit" function does a good job of this by just not adding the rows corresponding to the alternatives that are not present.