They absolutely can if that is what they have agreed with the DfT. Someone did point out that one philosophy is to try and push the Southern loadings onto Thameslink because of the fixed formation trains which can carry many people.
Which is essentially what has happened on GN. Once the Welwyn peak services return later this month, the GN-side Thameslink service is I believe at or virtually at 100% of the pre-Covid provision, both in terms of services and lengths.
By contrast, the non-Thameslink GN service is still heavily reduced. No peak Baldocks (6x tidal 8-car services per peak, plus three evening down services), all peak Peterboroughs missing bar 3, and all reduced to 8-car, all evening Peterboroughss missing, and the Kings Lynn / Ely service down to virtually solid 8-car. Perhaps more surprisingly, the 717 services will be remaining well down on pre-Covid.
Where this is causing some discontent is these extras tended to offer niceties like peak non-stop Welwyn North or Stevenage to King’s Cross. Commuters do like this sort of thing, even if the actual time difference is minimal. Likewise the ability not to have to board a service in the core. This certainly won’t be helping encourage people back who have a choice.
It will be interesting to see if the stored 465/2s return. My money is on that they probably won’t, especially as they’ve now gone from warm to cold store, but one never quite knows!