It's always been said that running two A/Vs simultaneously is a bad idea, especially if one of them has quarantine files, isolating dubious files from interacting with the operating system, the other A/V may well look to the first A/V as the source of those isolated files and begin to react against it, in short they'll work against each other rather before they'll compliment each other. That's just one example.
The other problem is linked to over exertion of apps running in the background making for sluggish computer use. This is why I often refer to MSE as capable A/V since it plays well with other protection essentials such as malwarebytes which can be run weekly to inspect for malware/adware/spyware which the majority of A/Vs will bypass when scanning, and browser plug-in essentials such as No Script and AdBlock Plus. If you can't see the malicious ads you can't very well accidently click on them, nor can they execute code from the browser with No Script.
That said, there is certainly no harm in running them independently, but you'll have to know when they are or are not active.