I had a VBA2C so its definitely possible with the right support. I had mine in an independent birth centre, however, the private OB I had before that was very supportive of them. Sometimes its worth looking around for who will give you the best opportunity.

BTW - if it helps, I had my first c-section in January 2007, my second in August 2008 and my VBA2C in November 2009. So very small age gaps