The reality of compensation is that, contrary to the expectations of virtually every tech employee in the universe, it is completely decoupled from job responsibilities and titles.
Compensation is set by supply and demand, and the way those forces augment or sap your negotiating leverage.
Almost every workplace in tech has some set of procedures for routinely adjusting compensation. If you're happy with your comp, you can let those processes grind in the background and get on with your life.
If you're unhappy with your comp, those processes are a trap, and you should (briefly) ignore them. Instead, figure out 1-3 strong arguments for improved compensation. Changes in job responsibility are one good reason; changes in the market are at least as useful. It helps to seem irreplaceable. The reasons you might be perceived as irreplaceable change from quarter to quarter; try to keep track of them.
When your manager appeals to them, politely dismiss them: say something like, "I understand why the system works the way it does, but in this case I think the system isn't capturing my current value. I like my work here too much to allow a process snag to make me unhappy. Because of [REASONS], we need to special-case this conversation. What arrangements can we make to work this out?"
Your manager doesn't want to give you an out-of-process raise. At least one of their reasons is valid: if they develop a reputation for giving out-of-process raises, the whole system goes to hell and the team becomes impossible to manage; perversely, being disorganized but occasionally generous with comp can increase turnover. Defense of process is likely to be your manager's primary objection to giving you a raise (the money probably won't be; it's not their money they're allocating to you).
So anticipate that. Be ready to negotiate for something other than an on-the-spot raise; instead, you can nail down a series of short/medium term milestones. "I'm at 85% of our benchmark compensation for my new role [note: benchmark comp is a fiction]. I'm new to the role, so I understand why you might not want to offer me an immediate improvement. All we need to do is bridge the gap between now and next year's review. Can we come up with targets to hit so that we can do an early review next quarter?"
On a good team, there is nothing your manager is more worried about than turnover: again, supply and demand. The naive way to exploit that fear is to get an offer somewhere else and use it as leverage. This will backfire; unless your management is not only excellent but also very, very in tune with your career (unlikely!), they'll just flip the "damaged goods" bit. They might placate you for a few months, but their new goal --- totally rational --- will to make sure you're not irreplaceable anymore.
So, like I said a few paragraphs ago, find a way to appeal to the turnover concern without putting a gun to their head. "I'm happy, but I could see not being happy in a few months if the situation stays this way" is a little on-the-nose, but it's better than (a) nothing or (b) an ultimatum.