East West Rail is the obvious service to extend west of Oxford - assuming 2tph on EWR, that'll be one to Reading / Heathrow? and one to maybe Bristol?
But Grove station was the immediate posts above mine, and until it's 4-tracked, I can't see that there's any capacity. Especially as the suburban electrics will be starting back from Swindon in the not to distant future.
Grove is in the middle of a 4-track section that goes from the proposed station site (former Wantage Road Station) to the site of the former Challow Station.
It is in a 4-track section, but two of the four tracks are basically used as extended freight loops, where slower trains (two or three at a time on occasions) can recess and await the passage of faster trains. I'm not sure opening a station on those loops would be a good idea, unless you provided additional crossovers within them, so there would still be capacity for parking up a freight and stopping a passenger train. Either that, or more provision for recessing slower trains, especially towards the Swindon direction. A similar lengthy four track section somewhere west of Uffington and then you might be talking.
I can't see the whole route as far as Swindon being four-tracked as some have suggested as there would be quite significant civil engineering needed.