Possible to play animations simultaneously (on same body part)?

Hi, I have a quick Q for more advanced Mecanim users (more advanced than me that is).

I have a dino that can look up, down, left and right. He also can bite. All animations that make the head move. I want him to target a specific position with his mouth. So let's say a target comes by from the left, the dino will bite to the left. This means playing the turn left and bite animation simultaneously. Is that possible?

So far I have a script that calculates how far the dino's head has to turn left or right (dot product stuff). I then use that -1 to 1 value to set a parameter in the Animator window. I use that parameter in a blend tree (blends turning left and right). So far so good. Now I want to add the bite part. If I play the bite after the left-right blend, the dino will look straight forward before he bites. I understand why that is. I just can't seem to figure out how to adjust this so that the dino will bite with his head to the left, and then go back to begin position.

Thanks for helping me out.