Can you conquer a battlefield multiple times per turn to trigger 'on conquer' effects multiple times?

Ruling: No, you cannot conquer the same battlefield multiple times per turn. You can only conquer a battlefield that you have not yet scored this turn.

Nuances:

• Conquering is defined as gaining control of a battlefield you did not yet score this turn
• You can only score once per turn, which limits conquering to once per battlefield per turn
• Even if you return your unit to base and move another ready unit to the same battlefield, it does not count as conquering again