The only 'buck' restrictions in IL, is that you have to have an antlered permit for each one, and that you can only take 2 antlered deer (one side of 3 inches or more) in a year (hunting year, not calendar) with all weapons/seasons combined.

There is also the 'cleanup' weekend in mid January right after bow season ends -doe only. It used to be handgun only, but now all 3 guns seasons allow you to use shotgun w/ slugs, muzzleloader, or handgun. The ML weekend mentioned in previous posts is ML only.

You can take as many does as you want to buy permits for, in bowhunting.