Per the docs discussion of multiple imputation,

Note that a call to the transform method of IterativeImputer is not allowed to change the number of samples. Therefore multiple imputations cannot be achieved by a single call to transform.

However, it is left unclear to the reader whether this typically means that multiple calls to transform should be applied (after changing the random seed each time), or separate fit_transform calls should be made (each with a different random seed), or whether either is equally-often the case.

Since a goal of multiple imputations is to know the uncertainty of each imputed value, and the value's imputation is subject to full model-fitting procedure, it seems that one would need to fully refit (via fit_transform) each time.