I told you I was going to post something so here it is, and sorry for the delay. As I said to you via email, you are not restricted to a proposal that is dominated by $\nu$. You could combine several moves with different proposals, not all dominated by $\nu$. This said, at least one of your proposals must be dominated by $\nu$ for the chain to be irreducible. You need to make sure that you have a positive prob. to visit all of the singular components (e.g. models). This is very similar to the within and between model moves in RJ-MCMC. In a sense, the between model proposal needs to be dominated by $\nu$. This is illustrated in the paper in several examples. Though, I agree that it may not have been terribly clear. For example, if you look at the paper, we have what we call the component-wise Gibbs, and the Gibbs. The component-wise Gibbs is a move that is not dominated by $\nu$ whereas the Gibbs is.

Anyway, I’d be happy to post more to clarify some more things if needed. I enjoy your blog, so please keep it up. I have added a link in the ISBA bulletin.

Cheers,

Raphael