You might find out the newly obtained puppy was chasing the
cat being surrendered whenever he would go by the litter box, or the episodes of urinating outside of the litter box took place
only after the
cat returned from outdoor adventures, or the
cat would soil in the hallway right outside of the laundry room where the litter box was kept (could the soiling be related to the
cat being
scared by the sound of the washer and dryer?).