HooBoy!!! The 9mm case is 0.001" bigger on the bullet end and 0.012" bigger on the primer end. So the .357 chamber being smaller (slightly) means that it could be 'opened' up a bit and tapered for the 9mm. That looks very promising.
That leaves action/stroke, etc. issues and the rim on the .357 case would make the magazine tube just a bit loose for the rimless 9mm case, but if every thing else is feasible, that's a minor issue.