I've done it. Especially early career, sometimes a better title is worth more than more money. I've also negotiated vacation time or work hours over money. And, sometimes I've hit the money request hard. It's depended on my priorities.
The problem is, you can't do ALL of these. Pick your top priority - money, time, title, responsibilities and open with that. Then, if you don't get exactly what you want, you can try for your second priority.
Ex:
Ask for $20k more than they offered. They say, well, we can give you $10k more. You say, I can make that work, but then I'd like three more vacation days. They say sorry, those don't budge. You take the job. Or they say, sure here's one more, you say great. If you had opened with your vacation day request though, you're not getting $10k.
You've also got to be prepared that they give you the full $20k you asked for, then you're done.