There's no precedent that requires one motion to be heard after the other. It simply is not the case. There have been many times when somebody has put their hand up, brought a motion, and it's been dealt with. Admittedly, maybe it was by the inadvertence of committee with those who brought motions previously, but nevertheless there is no established precedent that one be heard after the other.
You do have the authority and the jurisdiction, on page 1052 of O'Brien and Bosc, to hear this motion first.