In Boise we have this problem " EVERY" time our contractors build outside doors facing the oncoming weather.
My solution may not work for a triple door but for single doors I recommend putting a storm door on that affixes to the outside brick molding and keeps water from ever splashing onto the door and seeping through the gaps at the jab and threashold..
I have had so many floors get water damage from winter storms.
I wish I could get my contractors to put on even temporary storm doors.
Good Luck
Steve