spine-unity Runtime Documentation
There are multiple ways to accomplish this, but the easiest, by far, is this...
skeletonAnimation.AnimationState.AddAnimation(trackIndex, "run", true, 2);
You can call that directly after your "SetAnimation" call.
skeletonAnimation.AnimationState.SetAnimation(trackIndex, "walk", true);
"SetAnimation" will set the track selected to the animation you want, while "AddAnimation" will queue that animation on that track.
Whoops, Nate beat me to it. 😛