I only have info based on my experience delivering my mono-di twins 10 months ago. Though I'll gladly share. :)
I was fortunate to have prenatal care at one of the best of the best maternity hospitals around, and I really valued how much information and research was available surrounding multiple pregnancies, births, etc. when I was going through my pregnancy experience. Those covering my care dealt routinely with twins and more, which was great. With that said, I was informed it was considered standard-drill to be induced at the 37 week mark, though this was strictly with identicals and surrounding the risk for Twin to Twin Transfusion. Long story short (and in very much layman's terms...), once they're shoe-ins to be viable on the outside, they get them out and then needn't worry about TTT.
In my situation, I had a textbook twin-pregnancy, and through all my weekly ultrasounds they were sharing immaculately well, I was healthy, no BP issues, etc. so they allowed me to continue on and extra week. I ended up induced at 38 weeks, which I likely could've fought with little issue as things were still healthy, and going extremely well, though I hit a mental wall of "oh my god I'm huge and can't function anymore- get them out of me!".
So in this case, in this hospital, under this doctor's care, I likely could've gone longer again if I so chose. Get lots of opinions, and fight the good fight if you're really against induction. If any signs of TTT arise, or any other major issues, obviously things change. But please only pass that bridge if it comes. You know your body, and many people carry multiples in such a healthfully way and they're born as healthy, thriving babies, just as many singletons are.
And in hind sight- I would've shot down the induction. I was very fortunate to give birth vaginally in my labour circumstances- though I didn't give birth in a natural, unmedicated way, which was very important to me initially, and in not having that natural experience for myself and my babies I have had to go through a certain grieving period. In labour land, often medical interventions beget more medical interventions, and so starting off with an induction can lead a woman down a slippery slope.
A healthy mom and healthy babes in the end is most important though- go with your gut, don't settle for anything you don't believe in, and enjoy your multiples!!