Customized page

My website http://www.nieuwszicht.com is fine as it is at the moment but we’re looking to expand and have an extra backgroundpage with interviews, researches, more discussion, columns, quizlets and so on.

Therefore i need an extra layout option. Problem is that i can’t use pages like single.php cause they’re all used for the things iam using already. Everything is used.
I can also not just copy the index and edit it to my needs and upload it to a desired name cause wordpress doesn’t understand what theme it needs to use then.

Is there a solution where i can have my own extra page with all the functionality as used into wordpress?

Thanks a lot in advance