NYS Court once opposing counsel submits opposition papers to a motion, can they submit more opposition papers or a cross motion?

If there was a change in the motion hearing date, opposing counsel was never notified and opposing counsel responded with affidavit in opposition before the original return date can opposing counsel submit more opposition papers before the new hearing date? I want to submit reply papers to the opposition papers, but I'm wondering if opposing counsel will get another chance to submit additional papers in opposition or even cross motion either before or after I submit reply papers. Can opposing counsel do this upon finding out the new hearing date?