If you want to do that, there might be a business case for a new deep-level suburban rail tunnel from Soho/Kings Norton to Dudderston to remove the crossing chase and Cross City line services from New Street, which I would expect would free up 6-8 paths per hour per direction. This could enable a platform reduction at Birmingham New Street to increase line speed from 10mph to 25mph.
Timetable before infrastructure.
A Dutch version of how Birmingham New Street might work (post HS2 Phase 1):
Stour side
Platforms 1, 2 (eastbound) and 5, 6 (westbound)
- 2tph Manchester - Northampton fast
- 2tph Scotland / Wolverhampton - London Euston
- 2tph Shrewsbury fast - Birmingham International
- 4tph Chase Line - Birmingham International / Coventry stopping (routed via Soho)
- 2tph Shrewsbury slow - S&D - New Street - Aston - Willenhall - Wolverhampton - Stoke - Crewe (marketed as two separate services at Birmingham)
Platforms 3 and 4 for terminating
- 2tph Liverpool - New Street (terminating from the west)
That's 2 platforms in each direction for handling 12 through movements per hour and 2 platforms for handling 2tph terminating - pretty generous. 4C is spare
Gloucester side
Platforms 7, 8 (eastbound) and 11, 12 (westbound)
- 6tph Cross City
- 2tph XC South West - North East
- 2tph Hereford - Leicester - Cambridge
Platforms 9 and 10 for terminating
- 2tph Reading - New Street (terminating from the east)
That's 2 platforms in each direction for 10tph, which is again generous, and 2 platforms for terminating