If you want to stay and they want you to stay but their hr rules are limiting you to paltry raises, getting a competing offer could be what you need. That’s how I first broke six figures after 3 years at the same company.
But you can’t play that card unless you’re actually prepared to walk away if they don’t meet your expectations. And they can’t meet them unless they’re within their salary bands.
You can line things up with the band you’re in (or one they can feasibly promote you to), the offer you get, and the amount you’re asking for so you end up with a number you’re happy with when they top out a given band. And one you truly are prepared to leave for if they don’t.
But make sure that’s what you really want because you can definitely make more with less effort by actually moving.