Oh yes, definitely! I have precisely that in my flock.
There is one little five-year old EE who has always been a misfit, and last summer, the second to the youngest unit of four Sussex taught the youngest unit of five Welsummers to beat up little Flo by chasing her down and stomping her by dancing on her back.
I separated the Sussex into their own coop section and run, hoping the Welsummers wouldn't be influenced by them any longer, but such is not the case. Flo is still completely intimidated by them and if one chases her, she immediately squats out of abject fear and they then proceed to stomp her.
So, Flo gets carried from the coop in the morning to her own safe section of the run where she and her BFF, Joycie, a Brahma, enjoy peace and quiet together. Sometimes the two wish to be let out and the second they emerge, they get chased down by the Welsummers.
There's just only so much one can do to referee.