Terminating from which direction?
The west, primarily. You'd have to make the call as to whether creating two west-facing bays to give a U-shaped single platform surface would be preferable to retaining the flexibility to both terminate from the east as well as overtake services at he platforms, etc.
Once the SSL resignalling is done the nominal service pattern will be 16tph Hammersmith-Baker St (8tph H&C, 8tph Circle). Are you suggesting a Hammersmith-Paddington shuttle to bolster the western arm? that would be the only viable option but it's not hugely helpful in the grand scheme of things.
Depends how pushed for capacity the Hammersmith branch gets, doesn't it?16tph is a bit less than the planned 32tph on the northern Circle. Terminal capacity at Hammersmith would be the primary constraint on a Hammersmith-Paddington shuttle, but I think it would be worthwhile. As I say, I also would like to see the contention about stations east of OOC on Crossrail dealt with by building a new branch of the H&C alongside it to at least OOC (if not Ealing Broadway via Acton mainline or sharing with the Central out via Greenford) with stations at Royal Oak, Westbourne Park, Kensal, and OOC, leaving Crossrail to sail though whilst still serving those areas.
You can't run more trains east of Baker Street because the Metropolitan line services join, and short of turning Baker Street in to a terminus for the Met line (good luck getting that one past the consultation) you can't reduce the number of Met through services to Moorgate/Aldgate.
Agreed, unrelated to what I'm proposing
the flat junctions at Praed Street, Baker Street, Moorgate (for terminating services), Aldgate and Aldgate East all constrain H&C capacity far, far more than anything west of Praed Street. If you want higher frequencies, get a time machine and go back to ask the Victorians to build the entire circle as a four-track formation with grade separated junctions. That would let the Circle be an unbroken service whilst letting the other SSL services not interfere with each other.
Agreed, unrelated to what I'm proposing
I'm proposing turning Paddington H&C into another Baker-Street. TfL services from further afield would normally terminate in 14&15 (which should handle a fair few tph, being non-conflicting central terminating roads), and 16tph of through services would operate normally using 13&16. Basically, I'm proposing operating the H&C a bit more like the Met, i.e. S8s running out to West Ruislip or Ealing Broadway.
A future project to build a new tunnel from Praed Street Junction to Edgware Road would enable more through services to operate that far for interchange with the services there more conveniently than at Paddington, but you would struggle as IIRC, the best you could manage at Edgware Road would be 5 platforms, giving you just 3 down from the current 4 for terminating services from Royal Oak as well as High Street Kensington. I suspect just terminating at Paddington as proposed above would be the best you would get - I don't see Praed Street being sorted within my lifetime.