More than one page.php?

This may seem like an obvious question. I’ve created my own themes for sites that use all the same page design. Is it possible to use WordPress for a site that has a unique design for each page? Well, the header, nav and footer will be the same but nothing else. Is there a way to put in more than one page.php or is there another way? Or probably just creating each page in Pages section would work.

Always think of using WP for sites that have the same basic look so wondering if it can be done for sites that are mostly static, all unique pages and a page.

Thanks in advance. Hope this makes sense.