The issue is not so much the platform capacity for trains, but platform capacity for people.
Most notably
the narrow platforms next to the narrow stairs down to the Cooper's Row entrance. There's a queue to get to the stairs, which then creates a bottleneck on the platforms and risks people ending up on the tracks.
Obviously, if rebuilding the station further east it makes sense to have the possibility of more platforms.
is there something to be said for linking it with the Cannon Street services?
If physically possible to get down in the space currently occupied by Cannon Street station, fit a double-ending station in somewhere in between (preferably with some form of interchange with the District line), and then climb up onto the viaduct near Tower Gateway, then this far from a bad idea. Cannon Street is constrained more than Fenchurch Street by the terminal capacity, though this idea would probably mean segregating the CS network from the others (if not totally, then more than now).
It's the two stations with the highest percentages of walking onward travel (CS:80%, FS:58%), so tube interchange/Z1 penetration is not that important (CS:9%, FS:24%). And reverse-peak flows are likewise the lowest (CS:>1%, FS:2% in the am and CS:3%, FS: 6% in the pm), and would remain such - which would help with passenger flow - it's nearly all one-way (which will greatly help, though maybe it would have to be enforced and about 700 people will be annoyed in the morning, 1500 in the evening).
There's 2 problems though:
- 50,000 people will arrive in the am peak. I guess some Essex passengers might stay on to London Bridge, but that's it really. Paddington is going to be the busiest new-build underground Elizabeth line station with 174k/day (TCR 170k, Bond St 137k, Liverpool St 124k, Whitechapel 94k, Farringdon 82k, Canary Wharf 68k, Woolwich 56k), but it's not going to be as peaky. Maybe Paddington will end up dealing with 50k in the am peak, but with Fenchurch/Cannon Street seeing about half that in just the busiest hour, that's a lot of people on a 2-platform modern island.
- With that number of people leaving the trains, dwell time is going to hinder frequency - the busiest hour being 11,500 leaving c2c trains, 15,000 leaving Southeastern. Then again, we're looking at that being about 500 per train in about 60 seconds (looking at ~30tph), with (mostly) one-way flow, and metro-style trains. It might work.
(all figures 2011)