I see no persuasive evidence that the coin was struck more than once. The sloping edge with smeared reeding is simply evidence that the coin grazed the top of a stiff, but still mobile collar. A "forced broadstrike" in other words.
It's certainly not post-mint damage. The grading services have a habit of over-counting (and sometimes undercounting) the number of strikes a coin has received.
Of course that assumes they're even COUNTING the strikes a coin has received, something that is not in evidence. Where the potential fight begins is when we start to discuss whether that's a good thing or not.
Just out of curiosity, by looking at the dime I posted, what makes you certain that was done at the Mint and not after? What should I looking for exactly besides tool marks, in your opinions?
This is an easy one. The effect happens when a known fault happens in the known process of minting. In this case, the collar that normally establishes the rim of the coin has broken, in this case pretty completely, and the coin, nee planchet, has been allowed to expand beyond the normal diameter of the collar/coin.
The collar was not broken. The collar was fully intact. It simply wasn't fully deployed and it was pushed further down as the expanding coin grazed the top of the collar.