Capacity at Sheffield has been discussed here before, and any improvements to the north are going to be very costly. (likely in the 'never going to happen' category)
So a possible (simpler?) solution, London - Sheffield services and Nottingham - Liverpool services both enter and depart to/from the south. Could elevated bay platforms be constructed at walkway level at the London side. Its a falling gradient into the stations, so would actually be less gradient. There is the issue of a couple of overbridges close to the station throat, but if that could be addressed would it help? Advantage is you wouldn't be removing large amounts of bedrock.
This would free some platforms off, but I agree does nothing to increase capaity going north, but getting the two EMR routes separate from Northern, XC and maybe Hull Trains might help