I often have models or drawings that are not created in the same (/correct) local coordinate system. In Microstation application it is possible to assign GCS to those different files and then reference them with "GCS reprojection". Meaning that the GCS those models share allows for allignment of the models (who have different local coordinates / base point).

I would suggest to make this possible for each connector. Thus create a connector for each (set of) files that have a different local coordinate system. Now this part of the connector setup only says "GCS has already been set by ..."