@rrd+1h69msJL they absolutely offer counters. It all just depends on the situation.
Factor 1: does your manager think you are replaceable and do they want to expend their political capital to keep you? It needs sign off from a LL2 or 3.
Factor 2: the offer needs to be comparable. If you are a programmer and you get an offer to be a salesperson in a healthcare industry for $50k more a year and you have to move to a higher CoL area, HR won't be able to compute that. If your offer is same role for a competitor for more money and you aren't moving, they can absolutely compute that as "change in the market" and can counter.
Keep your eyes open for openings for your role at your big 3 neighbors. This is how you play that game.