Here's a rack that will do six.
I have no personal experience with this one and the fact that neither of the top two rack companies (Thule and Yakima) do a six bike rack
makes me think you should approach with caution.
[Link removed due to the old link being expired/stale.
The link was to a "Northshore 6 Bike Rack"]
I have seen, with mixed success, 4-bike bike racks where folks have strapped an additional bike into the mix.
Again, proceed with caution.
bicycles.stackexchange.com/users/1036/Ken Hiatt
I don't have any experience with hitch racks holding more than 4 bikes, but I do have an option that you may not have considered.
Forget the hitch rack and buy a small utility trailer.
Most hardware stores sell trailer frames like this to which you can add a simple plywood box enclosure ore something more elaborate.
It looks like the market for a 6 bike rack is fairly small, and the racks are expensive ($700+ US).
I am sure you could buy a small utility trailer for much less, you would be able to haul at least 6 bikes plus equipment and you would have none of the drawbacks of a hitch rack like: Difficulty accessing the rear doors of the vehicle.
Rattle, hum and road shake as the torque/lever forces shake the bikes on the rack.
If you decide to go the trailer route you can use plans like these to build your own PVC racks to keep the bikes upright.
bicycles.stackexchange.com/users/213/Gary.Ray
Keep in mind that hitch racks intended to carry large numbers of bikes (including the North Shore six bike rack) tend to require heavy duty 2" receivers.
Ensure your vehicle is properly equipped.
If you have room inside the van, you can use one of these to carry a few bikes (perhaps in addition to 4 bikes on a more typical hitch rack): http://www.biketote.com/store/category.php?category=12
I use the Bike Tote in the back of my Toyota Tacoma pickup to carry two bikes.
It works well -- it holds the bikes securely, and is very easy to install/remove the rack to/from the vehicle.
bicycles.stackexchange.com/users/2572/keithmo
The hitch is not designed to take the kind of forces that 6 bikes can produce.
A trailer sits on the ball and cannot twist the hitch, a rack adds twisting forces in all directions.
The end result (I have a mate who manages a bike shop) can be pretty expensive - like
the guys who's hitch (with 4 bikes on the rack) failed while being followed by a 30 ton B-Train.
Luckily for him the remaining scrap metal only damaged one truck tire - you would think the cost of replacing the bikes was all you need you worry about..... If you do, you need to strap the top of the rack to the roof of the car, and strap the rack and bikes to limit the twisting forces in the hitch.
The addition of 6 bikes on the back of the vehicle will also upset the balance.
Most cars have a ball weight limit - some as low as 60kg, few above 100kg.
I imagine your van is on the higher end of the scale, but 6 heavy mountain bikes + rack will be close to 100kg.
(if you are US/UK and think pounds, thats 130lb - 220lb).
You may find you are overloading the hitch and voiding warranty / breaking laws / voiding insurance There is a reason most manufacturers stop at 4.
Above 2, they almost always recommend/require straps and heavy duty hitches.
bicycles.stackexchange.com/users/3924/mattnz
Well, not to encourage spammers, but the Totem Pole is an interesting design.
It does have the advantage that the weight is carried fairly close to the vehicle, so there's less torsion on the hitch -- maybe this isn't sufficient to really allow the weight of 6 bikes to be carried, but it likely handles 4 better than the standard horizontal beam rack.
I would be a bit concerned about carrying the bike's weight solely from the front wheel, as this design does.
At the very least you'd want your bikes to have "lawyer lips", and on a long ride I'd be concerned about stressing/distorting the wheel.
Plus it's not clear (despite the cavalier statements to the contrary)
that bikes wouldn't bump/rub each other while being jostled on a rough road.
Also, the rack probably has trouble with kids bikes, since the wheels will not hit the bottom bar.
bicycles.stackexchange.com/users/1584/Daniel R Hicks
I also have a Sienna.
I put two bikes in upright racks on the roof.
And, as someone else said, can you put any inside?
That's what I usually do if I don't have people in the third seat; I can put four bikes inside if I arrange them carefully.
bicycles.stackexchange.com/users/4825/Joe Ganley
How can I fit 6 bikes on a hitch rack for my Toyota Sienna van?  Thank you!
How can I fit 6 bikes on a hitch rack?
bicycles.stackexchange.com
<car-rack>
bicycles.stackexchange.com/questions/9481
bicycles.stackexchange.com/users/4108/Bing
Most hitch racks are made for a maximum of 4 bikes. There also regulations relating to how much a vehicle can carry. For transporting 6 bikes a small utility trailer would be better. An alternative would be to put some bikes inside the van and the others in the rack.  A hitch ball is usually not designed to carry that much weight, and the car may be affected by the extra weight on the back. Overload the hitch may void the warranty and insurance or even be illegal. A utility trailer would be a safer option that could carry more than a hitch. The Totem Pole rack is one possiblity, but supporting all of the weight from the front wheel may damage bikes on longer trips. If you have room, you can put bikes inside the car and on the roof in addition to a standard hitch rack.
A hitch ball is usually not designed to carry that much weight, and the car may be affected by the extra weight on the back. Overload the hitch may void the warranty and insurance or even be illegal. A utility trailer would be a safer option that could carry more than a hitch. The Totem Pole rack is one possiblity, but supporting all of the weight from the front wheel may damage bikes on longer trips. If you have room, you can put bikes inside the car and on the roof in addition to a standard hitch rack.