With a family as large as yours, you would want :
1) Full Size SUV
2) Full Size Van
3) Large "mini" van (Odessey, Sienna etc)
While not only will you be toting 4 large boys.. potential friends but also their gear? Strong roof storage and large covered interior storage is also going to be important.
Also, getting LARGE folks into the back of a normal "car" door tends to me more cumbersome than in a VAN. Raised floors of the SUV and generally "low" cabins make it hard. Vans tend to have more Floor to ceiling room.
Hey - How about a Dodge/Mercedes/Freightliner "sprinter" van. Even comes with a Diesel!
http://www.mbsprinterusa.com/vehicles/passenger-van/
A Pilot/ MDX etc or the mid class size tend to have ZERO room behind their 3rd row seats. A minivan will be quite large behind the 3rd row. Full size SUV/Van is also pretty big back there.
On the other hand, you might consider just
how often the WHOLE family needs to travel together. Sounds like at least 2 kids are of driving age and the others are close to it. Maybe cheaper overall to travel in 2 more efficient vehicles than 1 really large one.