With the same software?  Im not sure you can have 2 different firms using the same program.

Maybe you need to explain your situation more?

Well, certain days of the week I will work in one tax firm and other days I will work on my own tax firm. We both will be using Pro-Series.

So you are an employee of the other firm?

If so, as Lisa said, I don't think you can't license the software for more than one firm.  Assuming that is the case, you would need two computers.  One for your business, and a second one so you can install the other firm's Network Version of ProSeries that is licensed to them.

What if I use Proseries Professional for one and Proseries basic for the other?

I assume if you pay for two programs and discuss your specific situation with Intuit Support, you may be able to configure Pro for one firm and Basic for the other.  

This sounds whole thing sounds a little like the Titanic leaving the port - a disaster in the making.