pathfinder – Does the avant-garde style bonus stack with itself?

No, he can not pile up with himself

Bonus of the same source (exploit, spell, class ability, racial ability, etc.) never stack with themselves, as specified in the Bonus definition:

Bonuses are numerical values ​​that are added to controls and statistical scores. Most bonuses have a type and, as a rule, bonuses of the same type are not cumulative (do not "stack") – only the highest bonus awarded applies.

The important aspect of bonus types is that two bonuses of the same type do not usually stack. With the exception of dodge bonuses, most circumstance bonuses and racial bonuses, only the best bonus of a given type works. Bonus without type always stack, except they come from the same source.

So, using the same exploit twice will not grant the bonus twice. Likewise, using the Bull Force spell twice (even if two different casters do it) will not give a total of +8 to Strength.

Unless this ability specifically specifies that it is stacked, but these are rare. For example, the fleet feat.

To be strong or not, I would prefer not to suggest allowing an exception and trust (with a grain of salt) to the developer who wrote it to decide whether the feat is balanced or not. There are exploits with similar effects that call that they pile up, and a bunch of Help anotherFeats of type (-ish) that do not stack, and the advantage of this feat is to grant an ally the benefits of another feat for a ride (Lightning Reflexes), which seems balanced ( for an exploit). Especially if you consider that, despite the requirement, you do not have to use a heavy shield (it could be a tower shield) and Avant-garde style bonus to multiple allies against a single zone attack.