Can I say "over-exceed"?

Let's say there's an accepted price range for rent. I would like to charge rent fairly, but I'm renting to a very wealthly individual. I don't mind exceeding the accepted range in my asking price, but I don't want to exaggerate and over-exceed.

Is this usage correct? In my searched I didn't find this phrase used. I don't think this is a pleonasm, because there are different levels in the excession, as I described above.

Edit:

I want something formal that I'll feel comfortable using in a user guide. I want it to sound professional.

Solution 1:

I'm renting to a very wealthy individual. I don't mind exceeding the accepted range in my asking price, but I don't want to overdo it.

overdo it: to do too much of something. There are always some students at parties who overdo it.

(What it is that might be overdone has to be figured out from the context.)

Solution 2:

While over-exceed could still be used, over-shoot or over-shot could be used as a better fit alternative. Hope this helps.