I thought I read that if you had drawn a Controlled Tag for a species, you could not have or apply for another Controlled Tag for the same species. This is from the regs, pg 82:
"Any person whose name is drawn in a controlled hunt for
deer or elk is prohibited from hunting in any other hunt
for the same species (archery, muzzleloader or general),
except when the hunter has been selected in a controlled
extra tag or depredation hunt drawing, or has purchased a
leftover nonresident general season tag for that species at the
nonresident price."
The only other exception is the Super Hunt, from their page in the regs:
"Super Hunt tags are in addition to any general and controlled hunt tags a hunter has applied for or may already hold. All other rules of individual hunts apply."
So, to me, you clearly are UNABLE to apply for or draw a second Controlled Antlered Only tag for any species for which you already have a tag, except for a Super Hunt tag holder.