It can be done. Add it to your list of things to do after you get the car operating properly. Along with disc brakes, 500 horsepower, overdrive tranny, a stereo and nice wheels. These are all things that can be done in the future as funds are available, after you have it on the road.
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1967 Parisienne 2+2 1967 Grande Parisienne
1967 Laurentian 1967 Strato Chief
Remember, "The Government" only has money confiscated from us.
You could change your diff to posi or you could look for a complete posi diff to swap in. Any thing is possible, comes down to how much money your willing to spend. Probably easier to keep an eye out for a complete posi dif. 10 or 12 bolt. and swap it in.