Kai'Sa Passive

Each ability has their own requirement: Q - Once you have enough BONUS Attack Damage you gain extra missiles W - Once you have enough Ability Power you gain increased base damage and some cooldown refund on champion hit E - Once you have enough BONUS Attack Speed you gain invisibility for a short time during the movement speed charging up period

You can have all three effects as long as you meet the minimum requirements and retain them. Your passive and ultimate I will assume have ability power ratios as well, so something like Hextech Gunblade and Rageblade with on-hit items could be worth while and probably the sources intended to get ability power from, since you want attack speed for your passive an on-hit/attack speed build would make sense to do.