Putting an extra pair of lines above the existing track is something that I've long wondered about.
But... to play Devil's advocate... You'd need some space west of Piccadilly next to the existing tracks for the two new tracks to climb high enough for the elevated section. Is there enough space for that?
Also, would a more cost-effective solution be to wait for the promised 'digital railway'? I'm guessing with that technology, you'd be able to easily run a train every two minutes or so each way on the existing track - especially given that you can expect every train to call at both Piccadilly and Oxford Road, so linespeeds between the two stations are never going to be very fast. Have two platforms each way at both stations (in other words, build platforms 14 and 15 at Piccadilly), and all you need to do is clear each platform within 4 minutes - which is regularly achieved at stations like London Bridge. Deansgate may be more of a problem if the station is retained with only some trains stopping, so maybe you'd still need extra tracks to separate fast and slow trains west of Oxford Road (or close Deansgate).
In fact, would a better place to stack some new tracks above the existing tracks be around the maze of junctions between Deansgate and Salford/Salford Crescent, in order to grade-separate all those junctions?