Activate Karn by paying ({1} magic symbol) , causing Staff of Domination to become an artifact creature until end of turn.
Activate Grand Architect's first ability by paying ({U} magic symbol) , causing Staff of Domination to become blue until end of turn.
Activate Grand Architect's second ability by tapping Staff of Domination, adding ({C} magic symbol) ({C} magic symbol) that can only be spent to cast artifact spells or to activate abilities of artifacts.
Activate Staff of Domination's first ability by paying ({1} magic symbol) , untapping it.
Repeat from step 3.
Once you have infinite mana, you may instead tap Staff of Domination using its other abilities if it does not have summoning sickness.
Results
Infinite card draw.
Infinite colorless mana that can only be spent to activate abilities of artifacts.
Infinite colorless mana that can only be spent to cast artifact spells.