If you move a unit you control out of a battlefield and move a different unit you control into it, does that conquer the battlefield again even if you already hold it that turn?

Ruling: No, you cannot score each battlefield more than once per turn. Moving a different unit into a battlefield you already control does not allow you to conquer it again.

Nuances:

• Moving to a battlefield you don't control does count as an open showdown
• However, it does not count as a conquer because conquer only happens when you gain control of a battlefield you did not yet score this turn
• Conquer and Hold abilities can only trigger when a battlefield is scored, which cannot happen more than once per turn for a player