If a question is of such high standards, and a bounty has already been offered and claimed, can I 're-bountify' (my word!) it?
Yes, this is possible.
A restriction is that if the same user places a bounty for a second time on the same question, then they must at least double the bounty from the first time (or put the maximum of 500 points).
Another restriction is that there cannot be multiple bounties on the same question at the same time.
Yet, other than that it is possible to place another bounty on a question where there already was one.