PCGS Submission Variety Attribution - Does it Keep Cert?

After speaking with several coin dealers, I’ve decided to submit my 1928-S MS64+ CAC Peace Dollar to add the VAM-3 Doubled Motto Variety Attribution. I do have a couple of questions:
If I send the coin in for the variety attribution and it is reholdered, will it retain its original certification number? Since the coin is CAC-stickered, keeping the original cert is important in order to have it re-stickered.
Can this piece be reconsidered + variety attribution/photographed while keeping the original Cert if the answer to above is Yes and it retains its original certification number?
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Reholder + variety should retain the original cert.
Recon should give the same cert, but I'm not sure on that. Regrade would be a new cert.
Reholder + variety will retain the original cert.
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