Equip Phases / Puresteel Paladin
You can shuffle around euqipment all you want with the Puresteel Paladin, as long as you have at least three artifacts in play.
The only restriction there is to activating the Equip ability, is that you can do it only any time you can play a sorcery (ie on your turn, in a main phase, when the stack is empty).
The rules on Equipment (specifically, the Equip ability) state nothing about how often you can activate it:

702.6. Equip
702.6a Equip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery.”
702.6b For more information about Equipment, see rule 301, “Artifacts.”
702.6c If a permanent has multiple instances of equip, any of its equip abilities may be activated.