Tie the kids on the roof and throw the bikes inside?
You can buy roof racks and trailer hitch racks, but I think the capacity is generally around 4 bikes. You can probably fudge a bit with small BMX style bikes. Or, take the tires off and squish the BMX bikes inside the car and the rest go on the rack.
An option is to get both a roof rack and a trailer hitch rack.
In the past, we've carried bikes in the back of a pickup. But, I think that was in an era when all the pickups had full 8 foot beds. Now, in general, the more passenger capacity, the less bed capacity.