The transmission on my "signature series" town.

The transmission on my "signature series" town car shifts rapidly back and forth between 2 &3 gears and 3rd and OD. Normally it does this after 12 miles in town driving at 40-50 mph.
However, it will also shift back and forth between 2nd and 3rd gear at about 30 mph. It does this only when the accelerator is slightly depressed in both conditions. When OD gear is shut down, it behaves normal in the 40-50 mph range. My mechanic is out of ideas. We have already replaced the old transmission with a remanufactured transmission and nothing changed. The engine check light is not on and I don't believe there codes available in diagnotics. What can you recommend?
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