Usually the breed of the chicken is not issue..it is the size..if they are more and less same there should be no further problems after the pecking order is set.
Sometimes if there is banties and large breeds mixed in same pen..the smaller size might become issue and they get bullied...but it is not usual response.
Yep..I would not hesitate to mix them up..you may need to do bit extra effort with food sharing first off...like hanging some greens from different places so they all are not fighting over the same bit..and maybe use few dishes for corn/feed. Once things settle down reduce the 'supply points' to normal.
Do we get to see some pics of new arrivals..? ;D