The best way to get solid wood thicker than 2" is to glue it up and mill it down to the size you need. Believe it or not, this is more common than you might realize. 

From time to time we do stock a few species of lumber in 12/4 thickness (2 13/16" thick).

  • Hard Maple
  • Basswood
  • Walnut
  • Cherry
  • Poplar

Thick hardwood lumber is quite uncommon for two reasons:

  1. It's hard to dry thick lumber; the drying process results in a lot of waste and degrade in thicker lumber. This makes it expensive and rare. 
  2. Low market demand

Glue up your own thick material when you need it thicker than 2". It will be more stable and you can get exactly what you want this way.