Some theoretical examples of Game Table Team-Up:
The Less Than All Possible Doctors
Let's say you have a Time Lord with multiple different incarnations, possibly even played by different people around your table. What could bring some but not all of them together? A bit of a crisis but not a universe-threatening super-crisis. An enemy of the current incarnation (or most recent at the table) moving back through his timeline to a vulnerable point in a previous life. Something Gallifreyans presumably can't do, as their travels synch up and they always seem to meet each other in the right order, unlike human or at least not-quite-Time-Lord archaeologists.
The Lost Companions
Missing your Time Lord type? Then maybe it's time for the companions to be separated from the TARDIS, in their home space-time or stranded somewhere or somewhen far away.
The Doctor- And Companion- Lite Episode
Reflect the series directly - the cast need a week off, so shift the focus. Take all the regular PCs out of service and bring in a small number of new PCs, who might get to interact with the regular PCs at the odd point here and there. Good for adventures with lower stakes and/or higher PC death tolls.