The idea of running multiple firewalls itself is not a problem.
In theory it can work, and back in my old days when I was very adamant about computer security I ran FOUR consequitive firewalls at the SAME TIME without issue or even noticable lag on internet connection.
I also ran lots of security tests on sites (that try to probe/access your computer and then give you the results of what they could/couldnt do) and it turned out that my 4x firewall combo worked against EVERYTHING those sites could throw at me.
Ofcourse I said 'in theory' because it is always possible certain firewalls will conflict with eachother.
The firewalls I used back then btw were: windows firewall, Sygate personal firewall pro, zonealarm pro and F-secure.