This may seem weird, but it is very much possible. You can dream as someone else or some other species too.
There was a chineese philosopher called Zhuangzi, who was butter in his dream.
Translation of his writings:
Once upon a time, I, Chuang Chou, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Chou. Soon I awoke, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things.
Zhuangzi or Chuang Chou's picture: