Can I finish cooking a pork roast next day after partially cooking it
This is an instance where sous vide really works well.
You can pre-cook your pork roast to 140 for 4 to 6 hours in the sous vide the day before.  Chill in an ice bath (still in the bag that you cook it in) to bring it down to safe temperature quickly, and then into the fridge.
the next day you can sear it in a number of different ways (broiler, on the grill, in cast iron, either whole or cut into chops and sear individually), and that should be plenty of heat to re-heat it nicely.