Do we know how many sets we are talking about?
Not too many, I suspect. But if the point of the exercise is to provide peak-hour, high-capacity queue-busters from and back to Birmingham, freeing up a few 168s to provide six-car trains for Oxford peak workings, which would then revert to running as two three-car sets to cover off-peak runs to both Oxford and Birmingham, they may not want that many Mk3s anyway.
If someone wants to try to work out the possibilities, this looks like the place to try
http://abrail.co.uk/lhcspassdetail.htm to find the codes for owners and operators see the menu here
http://www.abrail.co.uk/A quick scan suggests there may be about 20
TSOs▸ in store that aren't allocated to anyone.
DB» Regio certainly owns several spare
DVTs‡ and appears to own 10 or so FOs, though one or two of those are shown running with
W&S▸ . With W&S now running four-coach rakes (plus a DVT), not sure there's much scope for getting any coaches from that source.
W&S did say in 2008 that DB Regio owned enough Mk3s for it to operate five four-coach sets if needed, so maybe that makes one short set available for Chiltern plus whatever they can get running from the others DB owns, plus some of those in store - presumably subject to the prototype conversion proving a cost-effective exercise.