There are items that affect every single aspect of an ability BUT one: mana/relevant statistic cost. It would be an interesting set of items.
A missing possible defensive stat: resilience to debuffs and DoT skills...basically armor for debuffs...which would decrease the length of time debuffs and DoTs affect the champion.
If that defensive stat is introduced, another stat for champions could be introduced, especially those who USE DoTs and debuffs...not AP, but Potency, or some such word. Basically, more Potency, the longer your debuffs affect the target.
Another statistical possibility: increasing the AoE of abilities.
There's also no Aghanim's Scepter-like item...the scepter is an amazing idea...but I'd like it to affect the ultimates in ways other than damage:
Item Concept: (not all stats are necissary)
Cowl of Sarda, the Wizard Who Did It:
Alters Ultimate (different for each champion) OR Alters Passive
Examples of altered ultimates and/or passives: (It would only alter the passive OR the ultimate, so, while combining the two would sometimes be wicked...it won't happen)
Passive: Reduces the number of charges needed to activate OR applies a small DoT to every target affected by one of her spells.
Ultimate: Tibbers gains _ health, _ armor, and _ magic resist, and/or a taunt like ability.
Passive: Reduces the chance of double strike occuring, but changes it into a triple strike.
Ultimate: Significantly increases the chance of double strike occuring while under the effects of Highlander.
Passive: Raises the armor of the egg, and slows the attack speed of anything that attacks it.
Ultimate: Reduces the slow effect of glacial storm, but greatly increases the Area of Effect.