
That is what I did with my last overseas trip, as flying a dog excess baggage is very reasonable compared to cargo, and of course the dog is separated from you the minimum amount of time rather than several hours before and after the flight.
I flew out from Heathrow to New York - JFK, and flew back JFK to Brussels and drive and ferry home.
We did have an unscheduled stop at Dublin on the way back, but fortunately we did not disembark as she wasn't passport compliant at that point and would have had to go into Quarantine.