The handling will change yes going wider but in my experience the stock sizes did a fantastic job. The only best upgrade for tyres is using Michlin Pilot Road 2 to Road 5
Which such stickyness and quality michelin tyre, you do not need to worry about going wider , other brands always have “confidence” issues and are always twicy in wet winter days. Hence i will forever love michelins. Bridgestone is my only backup.