Your surgeon knows best based on your frame, if he said 340 then trust him, they know their stuff!!
There’s approximately 125-150cc in each cup size so that would take you just over 2 cups I’d say. They won’t squeeze any more in and if you’re looking for much bigger, you would most likely have to have another BA in a year or so when your skin has stretched so you can put bigger ones in.
Also bear in mind all surgeons have different opinions, so might be worth seeing another surgeon xx