Get a job offer from somewhere else that pays more. Redact it for source information and provide it during the negotiation. Explain that they can’t just match it, they need to beat it, or you switch jobs.
For whatever it’s worth, I’ve worked at places that have a policy that if someone starts looking elsewhere, they’re unhappy and are going to end up moving anyway, so they’ll just assume you’re handing in your notice. I don’t like this mindset at all, but I assume it’s fairly common.
Or maybe someone came across any actionable advice they’d like to share?