YES!
You're probably territorial of your home, or your bedroom, or your "special place" and if you had a stranger waltz in and claim it as their own, you'd be more than just a little ticked off.
If you'd like to get a second bird, you'll need to start with a second cage as well. Start with a 30 day quarantine (duh) and then slowly introduce the two birds. If they seem to get along well, you can then attempt (with strict supervision) to see if your old bird will accept the new bird into his/her space. It may have a happy ending, or it may be a disaster and you'll need to keep your new bird in a second cage forever.