Can leader/unique abilities "double dip?"

To emphasize what FailingCrab said: The keyword you are looking for is 'for each of the following'.
A search over all abilities reveals that there are currently 4 occasions in which the same (positive or negative) effect can be triggered and applied multiple times:

• Darth Vader - U- No Escape At the start of each encounter Darth Vader gains 8 Speed until the end of that encounter for each of the following: Empire ally, Sith ally, Jedi enemy, Rebel enemy...
  
• Emperor Palpatine - U - Crackling Doom While Palpatine is active, at the start of each enemy turn, they take damage equal to 20% of their Max Health for each of the following: they are Shocked; they are a Jedi; they are a Rebel...
  
• Sabine Wren - B - Blasters Akimbo Deal Physical damage to target enemy twice. This attack scores an additional hit for each of the following if the target: - Has less than 70% Turn Meter - Has less than 30% Turn Meter - The target is debuffed Hits after the first deal 75% less damage.
  
• Rey (Jedi Training) - B - Connected Strikes Deal Physical damage to target enemy. Damage is increased by 25% for each of the following: Rey has no debuffs; Rey has any buffs; the target has no buffs; the target has any debuffs.
  

If the keyword is missing (most occasions), an effect may be triggered by different conditions, but is applied exactly one time.

• Example1: Darth Vader - L- Inspiring Through Fear Empire and Sith allies have +30% Offense and have a 50% chance to remove 20% Turn Meter when they damage an enemy...
  
• Example2: Emperor Palpatine - L - Emperor of the Galactic Empire Empire and Sith allies have +35% Potency and 35% Max Health. Jedi and Rebel enemies have -35% Potency and -35% Evasion.
  Spoiler

  When an Empire ally inflicts a debuff during their turn, they gain 20% Turn Meter. When a Sith ally inflicts a debuff during their turn, they recover 20% Health.
  When a debuff on an enemy expires, Empire and Sith allies gain 5% Turn Meter.
  => The spoilered part of Palp's ability shows a second possibility of multiple effects applied for being both Empire and Sith. Since it is two separated definitions/sentences, it should be obvious and doesn't need the additional keyword.