Quick background - I am an accountant for a small labor union. The lady that runs the pension department is due for retirement and it is openly discussed in the office that I will be filling her role. I had planned to negotiate a raise when the time came, but my boss approached me the other day and volunteered that he would be giving me a raise when I moved into the new position. This was music to my ears, as I wasn't sure how well asking for a raise would go over, especially in the middle of a pandemic and after we just lost a major, multi-year pipeline project. I had a number in mind that I planned to ask for. If my boss offers me less than what I desire, would it be in bad taste to counter his offer?
It is absolutely appropriate. As a boss myself, I don't want ANYONE to be afraid to speak their mind and stand up for what they think they are worth.
If you worked for me and did that I would hear you out. If I agreed and had the budget I'd make the raise happen. If not, I'd explain my counter-argument and hope you stayed with the company without the raise. Or I would counter-offer a smaller raise.
In the end you have to be willing to walk if you don't get your number. If you aren't then you really have very little negotiating position and are demonstrating you are willing to work for less.