The following boards are unlockable.

Board	How to Unlock
Cardboard Board	224 stamps (8 boards complete)
Cheese Board	56 stamps (2 boards complete)
Deco Board	168 stamps (6 boards complete)
Future Board	6 stamps (6 Properties owned)
Ice Board	112 stamps (4 boards complete)
Jungle Board	84 stamps (3 boards complete)
Sweet Board	22 stamps (22 Properties owned)