My partner is second in command at his job, but they won't give him the official title/pay because it's not beneficial to the company to do so. He does the job because he genuinely enjoys it and honestly the only reason why he wants the title is so that he can have some actual authority. Imagine being second in command, but you can't reprimand anyone for doing screwy shit because you aren't technically a supervisor but when shit goes sideways, your ass is grass because it's your responsibility. That's what we're dealing with.
He gets a good bit of overtime which takes him from his standard 47k a year to about 55k. So to make things easier he went to the HR and his department head with this proposal. Give him the title so he can do his job effectively, don't worry about giving him the full supervisor pay of 75k, but cap him out at his 55k. The reason why he accepted this is because for the last three years, he's been getting about 55-56k a year due to all the overtime from covering shifts. He literally gave them an out.
They told him no because while yes he covers a lot of shifts and he does usually end up with that amount at the end of the calendar year, it's not guaranteed that he gets it. They would rather just pay him out in overtime than to give him the salary and the position title.
My head hurts from think about it all.