I cant find anything about this on the steemit white paper (page 9 is about steem power and powering down) and I cant power down yet so powering down is not my expertise, however you could try "troubleshooting" to find your answer....
Look at the image below If steemit lets you do this then, Yes there is most likely a second power down option that would power down whatever was earned since the first power down, and it would run separate from the first and has its own separate schedule.
(generated using my 1337 scripting skillz :P, not how the actual steemit website functions)
if there is only one cancel button then my guess would be there can only be one power down at a time meaning that if you were to click power down a Second time it would just reset the time with the current SP balance.