I am trying to figure out how to enable and disable only one interrupt at a time on Teency 3.5, because by using "noInterrupts();" and "interrupts();" all the interrupts are disabled at the same time.
Unsure if there is a better write up, but I think changing interrupt priorities would do what you want: https://forum.pjrc.com/threads/26397-Interrupt-priority-for-attachInterrupt
Idea being you lower the priority(bigger number) of the thing you want to stay out of the way and/or raise the priority(closer to zero) of the thing that needs to keep running.