Scouring Rage and Mighty Rage

Can you have multiple free actions off of the same trigger? Because then scouring Rage would become less useful as Mighty Rage lets you use a Rage action for free, and it just seems a shame that a fun feat suddenly collapses in use.

Source Core Rulebook pg. 17 1.1

Free actions use this symbol: <Free Action>. Free actions don’t require you to spend any of your three single actions or your reaction. A free action might have a trigger like a reaction does. If so, you can use it just like a reaction—even if it’s not your turn. However, you can use only one free action per trigger, so if you have multiple free actions with the same trigger, you have to decide which to use. If a free action doesn’t have a trigger, you use it like a single action, just without spending any of your actions for the turn.

That is a shame, Thanks for the help