What I would do to E N H A N C E Steam Achievements:
1) Session Achievement Summary: Give an option to make it so that Steam will show your achievement popups after you exit a game, with a popup window like the screenshot window showing a collection of the cheevs you got during that session, your already earned cheevs and cheev tracking for other ones. This could be in addition to your cheev popups during game or to take the place of them (so they don't show at inopportune times if you don't want them to).
2) The ability to turn off Achievement popups separate from all other popups. Hell, allow it on a per-game basis.
3) Customizable Achievement popups (noises and animations). Make it open sourced like Steam skins, but also work with developers to create promotional ones, marketable ones, or order bonuses or whatever. Allow users to apply different cheev popups based on rarity of achievement or achievement value (think like the different donation jingles/animations that Twitch streamers use).
4) Assign 1000 points to each game/application that divides the value of the points based on a normalization of the rarity of the achieved achievements. Gives people that Xbox-style race for points if people want to. Sure, Steam achievement unlocker breaks this, but achievements are ultimately worthless so who cares.
5) Create an API that developers can implement that allow users to create their own community achievements to challenge friends or Steam groups or whatever. It would just hook into different variables in the code and allow unlocking when conditionals are hit. Probably a bit too pie-in-the-sky, but it might be neat.