Depending on the minivan, you can put a fifth bike inside. I had a Ford Aerostar (stop laughing) that did not have a middle seat, but the mounts were designed to accommodate the third row seat on the middle row. I ended up with a five passenger minivan with a large cargo area. My current 1st generation Odyssey came with the second row option of two captain's chairs, giving my only four passengers with the third row folded down.
I've only got two kids, and will not be having anymore. Right now, my Grabber three bike rack works perfectly. Once the baby goes onto the trailercycle, I'll be using the custom interior rack I fabricated for it with the outside rack.