Scott,

I don't know about no more than once. It is theoretically possible, but the computation is a bit big for me. No more than twice is definitely possible. Split your guys into two groups of 16. There is a schedule in the archives where 16 players play in four foursomes so that every pair is together exactly once over 5 weeks. (Search the archives for golf 16.) Use these as your first five weeks. To get the next 5 weeks, split each 16 in half and form two new 16s by combining opposite halves. Then (renumber the players and) use 3 weeks from the same 5 week schedule as before.

Have fun.
--Victoria