HS2 probably won't reduce the number of trains in the existing station much as most of the 3TPH London and 2TPH Birmingham will still be needed to serve intermediate stations. Capacity of the classic lines will actually increase as the fastest trains will be making extra stops so have an average speed closer to the slower ones.
Six tracks eastwards out of the classic station could then probably handle 50-60TPH in total so even in its present configuration Piccadilly could be acting as a constraint, especially if longer trains mean less double-stacking in terminal platforms.
The maximium number of services that are ever likely to be needed from Piccadilly South / East even with massive growth are:
2tph to Leeds
2tph CrossCountry
1tph to Cardiff
8tph to Manchester Airport (Express)
4tph to Sheffield (Express)
1tph classic compatible HS2
4tph to Glossop
4tph to New Mills Central / Hope Valley stopper
4tph to Hazel Grove / Buxton
4tph to stopping service to Macclesfield / Stoke
4tph to Altrincham / Chester / Crewe via Middlewich
4tph to Crewe via Manchester Airport
4tph to stopping service to Crewe via Stockport
And finally if no tram trains:
4tph to Rose Hill
In total that is 50tph: 12tph to the airport, 24tph through Stockport (significantly above realistic potential line capacity) and 14tph through Ardwick. Realistically Stockport probably has a maximum capacity of 18tph, reducing that total to 44tph. In this circumstance 12 terminating platforms would be needed but it is a ludicrously optimistic prediction of future services.
Tram Trains could replace Glossop and Rose Hill (and limit New Mills Central to 2tph). That reduces the maximum number of trains to 34tph. If 16tph used 4 through platforms, 18tph is probably still too much for 7 terminating platforms without double stacking.
I can see the point of adding 4 seperate HS2 platforms but I very much doubt rail growth will continue to the point were 4 HS2, 4 through and 12 terminating platforms are needed without a major tram, train, or Tram-train infrastructure project being built. 20 heavy rail platforms would make Piccadilly nearly as big as Waterloo!