Old Oak would have had two dedicated 'international' platforms in the station box. Retro-fitting these later would be a pain.
However that'd be a doddle compared to retro-fitting a junction cavern to the HS2 tunnels between Old Oak and Euston...
In a retro-fit, it'd be a hell of a lot easier (expensive, mind) to run a new tunnel from Old Oak Common to the St Pancras approaches and put your junction above ground there - there's already a connector from HS1 onto the NLL there, which is almost unused (there's an occasional freight, I think, but rerouting a long-distance freight isn't a killer). You could sever the link to NLL, and run that connector into a tunnel portal (you'd have to rebuild the viaducts that currently run from HS1 to NLL and knock down a couple of industrial units, but no housing - there's just about enough room to get under the MML). In effect that would extend
HS1 to Old Oak, and then you could run international services from Old Oak or HS2 through it, though they couldn't stop at St Pancras without adding a reverse curve that I'm very doubtful there is room for. You'd probably build this as a single-track tunnel - it's only about five or six miles, which should be capable of at least 4tph each way, and I can't see you having demand for more than an hourly service.
But I don't think there's enough demand to justify this; a better connection between Euston and St Pancras would allow for a much more frequent service on net - from (for example) Manchester, you'd be able to get a 3tph service to Euston combined with the hourly Eurostar to Paris or the (roughly) 1tp2h to Brussels. No way can Manchester justify more than a tiny fraction of that direct to Paris, and not being able to carry either Manchester-London or London-Paris passengers on a Manchester-London train means that you'd have to have Manchester-Paris direct passengers only (you could do pickups at Birmingham Interchange and Old Oak, but that doesn't make enough difference: two to four trains a day would be the limit).
There are only two ways this makes sense. One is something like Euston Cross, combined with a massive change to the security/immigration rules on the Tunnel, to allow for a through train to run Manchester-London-Paris, at which point all of the Eurostar services are joined with an HS2 service and extended up the country. You'd have to allow Manchester-London and London-Paris passengers to use the same train, and the Manchester-London bit to be like a normal domestic train.
The other way is if there is lots of demand for domestic services through the link - but there isn't; because if you're on a GA train coming from Essex or Norwich or Ipswich or somewhere, then your better option is to change to Crossrail at Stratford or Liverpool Street and get across to Old Oak compared to walking through Westfield to Stratford International, and if you're coming from Kent, then you're going to have to change at Ebbsfleet or Ashford unless you live there (no way are they going to put shoes on an HS2 CC train and run them around Kent). And if you're going to have to change anyway, then changing between St Pancras and Euston isn't enough of a difference that avoiding it is going to be a huge traffic generator.
Maybe I've missed some huge destination in Essex or Kent that would transform that, or some proposal to build one. If Ebbsfleet Garden City is going to have a million homes by 2040, then, sure, build the link. But the last number I saw was fifteen thousand.
