These are the three new Illuminated groups from the article "More Groups Illuminated" by Russell Grant Collins in Space Gamer #72.

The Illuminated IRS

Power 7/7. Income 4.
Special power: Once per turn may suck the money from any one non-Illuminati treasury (in its own power structure or another's) to its Illuminati treasury. This counts as an action.
Special Victory Condition: Gain control of groups with a total income of 30 or more (including its own).

The Illuminated Moral Minority

Power 7/7. Income 9.
Special power: +3 to control any Conservative group; immune to any attacks from Communist or Weird groups.
Special Victory Condition: Control five Conservative groups.

SSFTASS

This group isn't in any of the Illuminati games. It is mentioned in the works of Robert Anton Wilson that helped inspire the game. I thought that it'd fit in the games as well. SSFTASS stands for the Secret Society For The Abolition of Secret Societies.

Power 8/8. Income: 9.
Special power: For 5MB may cancel any other Illuminati group's special ability for one turn. Does not count as an action, and can be done during another player's turn.
Special Victory Condition: Neutralized thirteen groups owned by other players. (Dropping your own groups doesn't count.)