No, because we already track if you vote or not. Here is an example procedure:
Each time Agnes Nitt sends in her vote, we put the sealed envelope in the Agnes Nitt pile. This is what we do with or without repeat voting, because it is illegal for Agnes’s vote to count twice - we must record that she voted!
Each time Agnes Nitt sends in a new vote, we incinerate any envelopes in her pile (unread) and replace with the new one.
When we hit count time, whatever envelope is in the Agnes Nitt pile is handed to the vote counters, in exactly the same fashion whether or not we have repeat voting.
The issue with point 3 is the vote would no longer be anonymous
No, because we already track if you vote or not. Here is an example procedure: