If you control a battlefield at the start of your turn, then move your unit away so it becomes empty, can you move another unit there and gain another Conquer Point during the same turn?

Ruling: No, you cannot conquer the same battlefield twice in one turn. You can score each battlefield only once per turn, and conquering counts as scoring.

Nuances:

• Even if the battlefield becomes empty after you've already scored it, you cannot score it again that turn
• This applies even if you use a different unit to move onto the battlefield