This is difficult to do, because the items ids, collections id, files id, element ids, etc. will have collisions, so the three database should be checked manually for that before. Anyway, it’s not really possible to manage different themes, access, headings, url, etc with Omeka.
This is possible with Omeka S, that is natively multisite and allows to manage content in one place, with any themes and collections you want (and a lot of other qualities, like natively web semantic and multilanguage). it implies “only” to adapt your themes and upgrade your plugins, if not yet ported (or ask somebody else). So it’s a lot simpler to do the migration directly to Omeka S than to do a hard custom and hard to maintain custom Omeka Classic.