It really depends on your existing pets. There is really no telling how they will react since every one of them can be different.
Some species of pets aren't exactly territorial or aggressive.
What are your current pets anyway?
Did you get all your existing pets all at once? If you introduced them into your family one by one, did they have the history of disliking the new comers? If not, I very much doubt they will start to acting rude now when they are older. Usually the younger pets have worse attitude. Old pets are usually more timid.
You can certainly try to introduce a new pet by bringing it home for a day and check out the reactions.