Any need for Phono stage with Brio

Is that a typo? Because it feels like you're asking about a better phono stage while saying MM when you already have a MM cartridge.
What exactly is the question?

The Brio has a pretty good phono stage.  The Phono MM would probably not be a big step up in quality (if at all).  You've got a nice, solid system there, and if you're looking for a better phono stage I would recommend something above the Phono MM.  

Best, Scott

The first question is how does your vinyl playback sound to you now? Are you finding flaws in the performance?

Second, will a stand alone phono preamp sound better than the built-in phonostage in the Brio? The answer is yes and no.
If you purchase an entry-level phono preamp or a mid level Rega, there would not be a significant increase in SQ. It’s a horizontal move.
For a significant upgrade, you would need to move up to the next level of sonic performance and build quality. Perhaps a tube phonostage would be in order.

With regard to your cartridge, you can do a lot better than the Elys. My advice is to upgrade to an external phono preamp when you're ready, but audition a couple at a retailer or purchase with a 30 day trial period.
Once you’re pleased with the phonostage, a cartridge upgrade should be next.