My first twin pregnancy was mono-di, we had our first u/s at 14 weeks, another at 16 weeks to check placentas, another at 18 weeks for anatomy, then at 20 weeks to recheck some measurements. At 24 weeks I had a shortened cervix, so had biweekly ultrasounds from there to monitor growth and check my cervical length. Went into labour at 38w2d, so....12 in all?
With my second twin pregnancy (currently in progress!), we had an early u/s at 8 weeks to make sure there was only one baby (HA!), another at 10 weeks to check placentas and chorionicity, then at 19 weeks for anatomy, again at 21 to recheck some measurements, then at 26 weeks, where I had a shortened cervix again, so I'll be heading back every 2 weeks to keep an eye on that and to check out growth as well.
I think the issue that more ultrasounds can lead to earlier delivery is because doctors always seem to think that at the first sign of anything even possibly off, the babies will be better off out than in. So they pressure you to induce or have a c-section. I would really do my research and make the doctors justify everything they want to do, especially when it comes to having the babies earlier than full term.