Jumping into n+k dimensions with k>1 in RJMCMC

Question

I'm studying the Reversible Jump Monte Carlo Markov Chain (RJMCMC) Algorithm for my master thesis. Basically it allows to simulate from posterior with different parameters spaces (i do believe). By searching everywhere i just found implementations where at every step the jump is done from spaces with n parameters to spaces with n+1 or n-1 parameters. I've been told that if i jump from a space with n dimensions to a space with n+k dimensions with k > 1 this won't be a Markov process anymore. I can't figure out why and there isn't much literature. I accept also answer just about the Markov process and not exactly speaking about RJMCMC