The phenomenon of parameter (structural) non-identifiability can pose significant challenges to the use of parametrized dynamical models. We demonstrate that, for the case of models being used to transform data across environments, it is possible to derive conditions under which the presence of structural non-identifiability does not hinder our modeling objective. We also show that when the non-identifiability has a certain structural feature called (thin) covariation, these conditions are violated, and the transformation methodology must be modified. We demonstrate these results on the problem of correcting batch effects in cell extracts, which are used as rapid prototyping platforms in synthetic biology.