Another classic scenario, you've gone and put a bunch of nice belly blendshapes on your model and now need to transfer them to the clothes. Don't do this work manually, let the computer do it! Use a wrap deformer, move the belly, then step the resulting cloth shape off as a blendshape/shapekey.
Maya notes: Make sure to turn "exclusive bind" on when wrapping the mesh or it'll fill up all your ram and crash your computer (don't ask me why), the blendshape deformer comes before the wrap deformer in maya's node graph, so duplicate the clothing mesh, delete history on it then use it as a blendshape target for the original.
Blender notes: this is called the SurfaceDeform modifier in blender. Apply it to the mesh you want to move, then just eyedrop the mesh you'd like to wrap it to and hit bind. Add a triangulate modifier to the source mesh if you're getting funky results (thanks fatback!) then apply the modifier as a shape key. You can mask the modifier to only a selected vertex group to localise the deformation.
Houdini notes: This is called the Point deformer in houdini, although there is a better version for CFX on gumroad named "wrap deformer".