Well not exactly a minivan but the Ford Flex is rated at 5000 lbs
Exactly, not a minivan, and most reviewers like it (well, so do I, but not my significant other). The old 4.2 Freestar was rated for 4000lbs, but that was another hard-to-love minivan with a rough engine.
During service at the Honda dealership, I took a good look at a Pilot and it's incredible how cramped the interior is vs the platform-sharing Odyssey. Also, all reviewers complain that powered sliding doors on minivans are too slow. They aren't too slow : they are quite indeed too quick. Borrow three kids for a week and you'll understand