The one thing I would do is to disable MSE. Microsoft even recommends the use of a third party antivirus. And it presents a conflict.
http://www.howtogeek.com/173291/goodbye-microsoft-security-essentials-microsoft-now-recommends-you-use-a-third-party-antivirus/

As far as the other security software you have they all play well with avast.
Just be sure Super Anti-Spyware is “on-demand” only and not resident due to possible conflicts.

Here is what I have; avast free, Comodo Firewall w/D+, MalwareBytes Premium, Super Anti-Spyware (on-demand), MCShield.

@ srome Everything is okay as long as SAS is “not” resident. And not any of them do the “exact” same thing.