Can You Run Malwarebytes With Another Anti Virus Or Anti Spyware Program Already On Your Computer?

I’m thinking about ditching Windows Defender because I know it sucks, and it came with Norton Internet Security 2008, and I know I have talked bad about Norton, but they have improved greatly from the past, and it doesn’t slow my laptop.
I’ve read and heard so many great reviews about it, so if I have Norton, Super anti spyware, can I run malwarebytes along with them?

What Is The Best Anti-virus/anti Spyware/firewall Package?

I have a normal home PC that 2 children have access to. We have been getting lots of malicious web sites popping up and currently only have free software (Avira Antivir and SUPER Anti spyware) and the windows firewall. I have heard that AVG is good.