You can but it probably won't do what you want. The purpose of a PID (or a PI) is to make the input error signal go to zero. Unless the process is unusual, there is not value of the sum of the two PID outputs that makes both errors go to zero at the same time. If they don't, the PIDs will keep searching and will fail.
Design your layout this way. You have two error signals. Write the equations of the process (not the controllers) needed to make both go to zero.