Is there a counter-example showing that Morley rank in the theory of compact complex spaces (as defined by Zilber, Pillay, Moosa, ...) is not definable in families?

Given the existence of such a counterexample in DCF (constructed by Hrushovski and Scanlon; it is a family of Abelian varieties) and the similarity between two theories from the model-theoretic point of view, I am inclined to think that there should be a counter-example in CCS. But I have difficulty "translating" (at least straightforwardly) the DCF example into the CCS world since it uses some facts, such as existence of certain definable families of polarized Abelian varieties, that I am not familiar with.