If they are pretty much the same size or gentle temperament then yes go ahead and mix. I have several breeds together in my laying pen. I do have silkies that are by themselves because I had them with another larger breed and the roo started picking on the silkies. Silkies can have vaulted skulls so they can be easily injured if pecked in the head so I keep them separate.
All mine get along okay. But most are dual purpose sized with nice personalities. My GLW are bossy, but everyone else lets them be in charge, so its all good!
My egg layers, which I have about 50, are different breeds and mutts all mixed together. They get along well. Each bird knows their place in the pecking order. Each spring I add a few more with no problems.
They can. Just don't mix aggressive and docile breeds. For example -
Don't put faverolles in with RIR.
Don't put polish in with Leghorns.
Don't put cochins in with Wyandottes.
That being said, sometimes those breeds aren't as aggressive if you get them from a reputable breeder. But I still wouldn't try it. I lost two birds that way; trying to mix more aggressive breeds with less aggressive ones.
The only docile bird I ever had that could hold her own with the RIR, sexlinks, and Wyandottes was my Australorp.