Hi Sean,
A nice 11 round schedule is possible and
there is an example here. It has the property that no two players sit down together at a table more than once, so it has optimal social mixing. Because of this property you are free to assign the groups of 4 to partners and opponents at random, however you do it, a players 11 partners and 22 opponents will all be different people. I would use this as the basis, and then add a few more rounds if you want them.
Hope that helps,
Ian.
