Is there any reason why I wouldn't want to start the ADC from within it's IRQ?

I have 3 inputs I need to sample every n minutes. I have an n-minute timer that can kick off the first one, but I need to run the second and third samplings in succession after that.

Is there any reason why I can't have my IRQ handler set up the 2nd and 3rd conversions, and call the final handler after the 3rd?

Specifically, I'm asking if there's any kind of race condition or order of operations I should worry about.