222% is what you get with 6E mods, using a CD set and CD primary on the triangle. That's it for what you can do with mods. (I believe it's 216% for 5A mods, but don't quote me).
Mods will not otherwise affect your CD. However there are lots of other ways to gain CD. Depending on the character, the Mastery stat you gain once you hit relic levels might increase a particular toon's CD. This is hard coded into the character, so either relic levels do affect CD for that character or they don't. You can't convert the toon into a type that gains CD via mastery, but if they do get that, you can control how many relic levels you give them.
Many leadership abilities also affect CD. I can't remember all the Unique abilities in the game, but I'm sure some of them also affect CD of not just the character with the unique but also other allies while the character with the unique is active.
And, of course, some characters can grant CritDamageUP buffs. Some do this by themselves, others by copying the buff from another toon the way that GMY can copy enemy buffs and spread them, or the way that Fulcrum can copy ally buffs for herself.
