Is it possible to install WordPress MU on a subdomain?

Yes is possible. The only thing is that you will have “two sets” of permalinks:

  • example.com/2015/07/27
  • example.com/new-website/2015/07/27

Here is a codex article that explains that.

Edit 1: Here is a more detailed article on the topic with it’s pros/cons and potential issues.