If using IGES or STEP to export from the CAD package, save the assembly to a single file and then use STAR-CCM+ to read the in the geometry and translate the surface. At inter-region boundaries, STAR-CCM+ automatically detects surfaces that are within close proximity and attempts to merge them, resulting in a common boundary definition at the interface (note that this may not always be successful). It also provides the option for generating feature curves. The boundaries can then be separated out to interface and non-interface groups and duplicate copies made of the boundaries at the inter-region interface. New regions can then be created thereafter which will have the same triangulation for the boundaries at the interface. A single mesh continuum can be used to volume mesh the entire geometry, resulting in a conformal mesh at the inter-region boundary interface.
Is you save the individual parts in the assembly as separate IGES or STEP files, then on importing them into STAR-CCM+ (either at the same time or one after the other), you will get the choice of whether to create one region per body, one region per file (recommended) or one region for all files. Regardless of the option selected, you will eventually end up with individual regions with triangulation at the inter-region boundaries being (most likely) different. For the most part STAR-CCM+ can deal with the different inter-region boundary triangulation by using the edge zipper to match the perimeter triangulation and then deleting one of the boundary pairs so that a conformal mesh interface can be created between regions. However, depending on the variation in perimeter triangulation, the edge zipping may fail and you will have to use a different mesh continua for each region, resulting in a non-conformal volume mesh interface. For this reason, it is recommended that you use the first approach discussed above to simplify the meshing process and guarantee a successful conformal interface.
Note that in general, you are better off importing a Parasolid Transmit file in preference to an IGES or STEP file when dealing with assemblies/multi-region cases. A cleaner translation is usually achieved via Parasolid, resulting in less setup working being required.