You'll be able to set another bounty after the present one expires or is awarded, subject to the restriction $$\text{new bounty}\ge \min(\,2\cdot\text{previous bounty}, 500\,)$$ At present it is not possible to change the amount of the bounty after it was set. And I don't see a convincing reason to add such as feature.
It's one more link to include in the interface, one more dialog window to design, and more code to maintain.
Also consider the added ambiguity concerning whether or not the increased amount means the bounty period is renewed, and ensuing questions on meta sites. No matter which way it is, and no matter how clearly the rules are stated, some users will expect things to work their way, and will launch a debate arguing their case. Witness the unending meta.SO questions about why fruitless bounties are not returned, and arguments over whether they should be.