Yes you can have Norton and Malwarebytes without issues.

I use NIS2009 with Malwarebytes and Spybot S&D and also SuperAntispyware. You may also look into Spywareblaster. Another security utility that I think is a necessity. SpywareBlaster® | Prevent spyware and malware. Free download.
All of these will work together without issues.

Ccleaner is a great little clean up tool. It's not a security utility. I use it several times a day just to keep things tidy.
Good Luck.

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