This question is related to this one: http://mathoverflow.net/questions/145934/local-smallness-and-higher-topoi which has not yet been answered.

The $2$-category of topoi and geometric morphisms is not locally small. (As I mentioned in the question above, for example, if $A$ is the classifying topos for abelian groups, the category of geometric morphisms from $Set$ to $A$ is equivalent to the category of all abelian groups, which is not small.)

**Question:**Is the $2$-category of topoi and *only etale geometric morphisms* locally small? 

Note: I'm actually interested in the corresponding statement for infinity topoi.