MurphysParadox |
Yes. The Adaptable Luck is a luck bonus. The other inspiration spells provide competence bonuses. Since they are different types, they stack. What wouldn't stack is timely inspiration + gallant inspiration.
You can also use them on the same roll as all three can be done retroactively and adaptable luck does not take any action to activate. Again, you can't use both timely and gallant inspirations yourself, as you only get 1 immediate action a turn and thus couldn't cast both at once (and wouldn't want to anyway since they don't stack).