How to manage multiple clients website having same code structure but different UI?

I want to create websites for many colleges using MVC.
Since coding structure will be common for all the client websites but the website templates will be different I need suggestions on handling this.
Do I need to create a core framework for this and use the same for other website projects? If I do so, then how do I handle the website template as these will be different.
Any opinion will be a great motivation for me to start.