Hi Sarah and Welcome! Thanks for stopping by to ask your question!
I have had 3 C sections as well. First was an emergency, second was a VBAC attempt that didn't fly... and 3rd, like you, was scheduled as my doctor wouldn't support a VBA2C (and it didn't make sense in my situation anyway.) We have always known that we wanted a large family and I've always been concerned (even from my first C section!) about the question that you are asking!
Many doctors get a little skiddish about more than 3 C sections. It is a more difficult procedure because of scar tissue and I think the less experienced surgeons are worried about their liability. (My opinion) However, from conversations with my doctor and the research that I've done, the real risks of an increasing number of C sections comes from placental issues - previa, accreta, etc. than from the actual operation. Scar tissue does increase with each C section that you have, but doctors can "clean that up" when they're in there and it will only cause a problem if there is a very urgent medical situation and baby needs to be removed stat.
It's important to ask your doctor about the state of your uterus after your next C section. Depending on how you heal, the tissue can weave together (like your outside normal skin -- basically going back to normal, or sometimes it becomes very thin as it heals. There are stories of women who've been opened up and doctors can see the baby through the uterus before they've done any sort of incision. This is called a window and I believe it's very rare. The doctor should note in your surgical post op report how "things look in there." My doctor actually told me on the table that I had a very "sturdy" uterus.
If you are getting push back from your doctor on having #4 (if you do want one!) I would recommend getting a second opinion!! There are many, many women who have had four or more C sections... hopefully some of them will check in and pop up to give you their advise!
Good luck with your upcoming birth!