Answer that already won one bounty won't be eligible for automatic award of second bounty. Taken from the faq:
What is automatic awarding?
Approximately 24 hours after the end of the bounty period, if the
bounty starter has not manually awarded the bounty, the bounty may be
- The answer must have been given after the bounty was started
- The answer must have a score of at least +2
- The answer must not have been written by the bounty starter
So the only option is if the user starting the bounty is manually awarding the bounty to such an answer, and this is possible indeed. See this answer as a proof: it was awarded two bounties as can be seen in the bounty score tooltip: