If it stacks with the weapon's normal enhancement bonus (and it does), I see no reason why it wouldn't stack with other enhancement bonuses.
According to page 21 of the DMG , Bonus types of the same name do not stack. Therefore, if you gave the sword of Aaqa the chaotic bane ability, which would increase the +2 enhancement bonus of the Sword to +4 vs. chaotic, If evil bane were then placed on the sword, it would be an enhancement bonus of +4 to evil, but since enhancement bonuses do not stack, (i.e., magic weapon does not enhance a +3 longsword, p. 21 DMG) The new +2 chaotic bane, evil bane mithril longsword would not have a +6 bonus against chaotic evil outsiders, but would instead have a +4. Maybe I'm looking at the glass half empty, because I do see your perspective on it. That's just how I personally would rule on the bonuses.