The A321 is not wider than an A320. The A320 family[1] comes in a variety of sizes and configurations to support different profiles, but they are all variations in length, fuel capacity and MTOW.
Making a plane longer is relatively straightforward, just insert additional sections before or after the wings. Making a plane wider you may as well design a whole new aeroplane.
[1] https://en.wikipedia.org/wiki/Airbus_A320_family#Specificati...