Is there a way of transferring large numbers of picture files between two PSE catalogues without losing tagging information, or alternatively splitting an existing catalogue that has grown too large and retaining the same tags in each.
How large is too large? And what kind of tags are you talking about - keyword tags or People/Places/Events (system tags).
As far as I know, there is no limit to the number of media files you can have in a catalogue.
If you write keyword tag metadata to the file (using Ctrl+W), the tags will transfer between catalogues but will appear in an Imported keywords category unless you map them to a new or imported keyword hierarchy. People names will transfer to the Imported category but any face recognition that is associated with the tags will be lost and will need to be recreated. I believe there will be similar problems with Places and Events.
If you really want to split a catalog, probably the best way is to duplicate it and then remove media from one or both of the copies. This will preserve all tagging information.
But I suggest that you evaluate whether you need to split a catalogue.