You'd most likely need to fake it, using blend shapes or another kind of deformer (or combo of deformers) to get object A to move toward the shape of Object B, but then blend transparancy between the two objects.

Using particle effects and the like to help mask the switch can help the overall effect as well, depending on what exactly you're trying to do.

If you really want to try to make one shape blend into the other, you'd have the best results doing a blend shape, but you'd have to duplicate object A and then remodel it into object B without adding/subtracting geometry.