Handling REST with page url

Is there a way to process a REST based page url. Here is what I am trying to do:

I have the following wordpress page: https://www.counterjumper.com/blogindex

Currently I can pass a value to the page as follows https://www.counterjumper.com/blogindex?cat=category1

What I want to do instead is use a REST url like https://www.counterjumper.com/blogindex/category1

So my question is if there is a way to do this?