Always an interesting discussion on this, for a TOC that was spawned out of the original RR North East franchise and then grew in the west as well.
It's logical that the WCML service could move to the West Coast Main Line operator, and as for the rest, initial thoughts were that the Liverpool - Cleethorpes service could just drop over to Northern, as would the Huddersfield stoppers, but then that leaves the core North East service, which if moving to another TOC leaves just LNER or Cross Country as potential recipients
So, is the solution for TPE to carve up a small franchise and dump its remains elsewhere, or should it actually be expanded to pick up more services that meet the "Transpennine" definition. As per another comment above, Northern is unmanageably big, and so one solution could solve both problems.
Also, just because the current service patterns (Manchester to Leeds then four different destinations on the East coast) have been there for years, it does not mean they have to stay like that.
Potential additions could include:
*Liverpool - Nottingham (assuming the long discussed split of the EMR Norwich service does happen)
*Blackpool - York
*Chester - Leeds
*Leeds - Carlisle & Morecambe (remember, the pennines reach all the way to the Tyne gap)
As we are in the safe space of the speculative ideas section I post this in the hope of not getting shot down!