From the bounty help page:
- All bounties are paid for up front and non-refundable under any circumstances.
- Additionally, if you offer multiple bounties on the same question, the minimum spend doubles with each subsequent bounty (50 reputation on the first bounty, 100 reputation on the second, 200 on the third, and so on).
There's a minor exception to the bolded statement. Since bountied questions can't be closed by ordinary users, sometimes we will refund a bounty in order to close a question. But we don't have the tools to refund a bounty that's been awarded already. I can imagine a lot of mischief and bad feelings that could come from such a power, even if its users intended well.
You certainly can offer an additional bounty on the same question. If it's not available immediately after awarding your first one, try waiting a couple of days; the logic is probably like the logic which prevents a new question from being bountied immediately.