Humour me, but surely easier to upgrade the existing 3rd rail electrification than go to OHLE though?
I thought you were suggesting the only way to meet the power demands would be to go OHLE.
It might be easier, it depends on what power is available and where. It's not the best of ideas though, 750V DC is just so woefully inefficient. AC has losses of upto 5%, DC is upto 35%. That's electric being burned off into heat in cables, in the rails and in resistor grids during braking.
The existing third rail supply is based on a 33kV HV grid (Network Rail's grid, incidentally) which supplies to the 750V substations that feed the third rail.
If the 33kV grid doesn't have the capability to supply more substations, then 750V DC won't be able to provide the required power to meet the service requirements. That's the case in some areas, lack of 750V sub stations is an issue elsewhere.
There are three options, depending on what the precise power supply problem is - it could be as simple as providing more 750V DC feeders, it could need an upgrade to the 33kV grid to enable more 750V DC feeder stations, or move to 25kV AC with Auto Transformer Feed if required, particularly if it's not possible to do more with the 33kV grid.
If you're going to spend £26bn on Crossrail 2, it might be worth allocating a small amount extra to provide 25kV AC OLE on the full route, pretty much every unit working in the south by the time Crossrail 2 is completed will be 25kV compatible. Might be is the operative phrase here.