Make a few duplicates of your original first:

1. Model in symetry, so you have a symetrical blend shape, of lets say a smile.

2. select this symetrical smile shape and then one of the copies and make a blend shape.

3.right click on the model and go to paint> blend shape target weights.

you can then brush off part of the influence. delete history on the object and you have an aystmetrical shape.

Then just apply the symetrical shape again to another one of your copies and brush away the values on the other half of the face.