If that is what you are looking for, you might be disappointed as the improvements would be marginal at best by switching from 15 inches to 16 inches alone. I would say it would be for aesthetic purposes more than anything else.
Since the standard Corolla models (CE/LE/S) were more geared towards comfort, the suspension, steering, tires, gears etc, are all tuned for comfort and fuel economy. So that would require a bunch loads of changes to get the car to handle and be stable especially at high speed fast maneouvering.
Remember, since the diameter of the wheel is growing, you might need lower profile tires to keep the overall circumference of the wheel/tire combo the same.
If you must get slightly better handling through swtiching wheels, I would recommend getting slightly wider 16 inch wheels as the stock 10th gen 16 inch wheels are only 6 inches wide (go for 16 x 6.5 or better yet, 16 x 7) and a good set of summer tires that are lower profile (195/55/16 would be a good size and if you get 16 x 7 inches wheels then 205/50/16 would be the best option).
Thanks for all of the replies and help. I'm going to go with the OEM 2010 alloys. Had new struts installed today, the old ones were trashed, boots were rotten. The stock 15" wheels keep the vehicle from handling well, the new 16's will do wonders for that. Also looking for some projector headlamps (black), matching taillights, and blackout grille. Also considering upgrading the seats to leather. Car runs remarkably well for its age and mileage.