An idealised IterativeImputer would allow some features to be predicted as categorical variables (with a classifier) and others to be predicted as continuous variables (with a regressor) or even other specific distributions.

We could consider an interface to IterativeImputer that would allow users to specify the estimator used for a particular column selector, much like ColumnTransformer does with transformers.

On the other hand we may decide that this adds rarely needed power with excessive complexity.