You could do 5 pools of 5 on Saturday, with the top 2 pools
being "power pools" with the 10 best teams of your
tournament. The other three pools are formed using snake
seeding of the remaining teams.
On Sunday, all 10 teams from the 2 power pools advance to
bracket play with the top 10 spots, with the top 2 teams
from each of the other 3 pools also advancing to bracket
play. You'd then have a 16 team bracket and can play it out
like normal. The bottom 9 teams can play various consolation
games, scheduling in such a way to avoid any pool play
rematches.
-Mark