Is it possible to blend Animations in a way similar to Blendshapes?

We are working on a project in which we need to be able to dynamically control how far the limbs on a rigged model are able to move in various predetermined directions. For example, from a T-Pose, raising the arm to be vertical would be the full range of motion, but we would like to be able to specify that the rig assumes a pose halfway between the two, or maybe 20% or 80% of arm raised. Much in the same way that you can influence the weights used for blendshapes, I'd like to be able to control pose weights.

If this cannot be done, then I need an alternative way to programmatically create a pose.