You actually can do this, I've met people that use this strategy. Here's the catch, generally you aren't in their system, since passports are very complex, and from what I've heard the EU isn't very good with keeping track of all of it. BUT if you get caught you can get blacklisted from visiting again.
Along with a fine, and possibly seeing a judge. This isn't legal advice, but really better off not doing this. You may get away with it for a bit, but the problem you'll run into is when you get blacklisted on BOTH passports for 5 years or whatever they decide.
I've seen other travelers get penalties ranging for 1 year to 10 years of no entry, in various countries due to messing around with visa laws. It's ill advised in any country, not just EU zone travel. The penalty obviously depending on the issue.
There are many legal and legitimate ways of extending your visa past the 3 months in, 3 months out rule that they impose. You can sometimes take as little as 1 class and qualify for a longer term visa in some EU countries. Other places will give you residency for starting a business. There are options. And using the dual passport "trick" could end up with you being in big trouble at worst, and running the risk of being blacklisted at best.
TLDR: Not advised at all.