Can You Redirect Every Existing Html Page Through A Php Function?

Is there a way to redirect every single page on an existing web site through
a php function?

In other words, say I have a whole functional HTML web site, never written
to use any php. Now I would like to have a php function handle displaying
every page, for example, instead of:

http://www.mysite.com/mypage.html

you would call:

http://www.mysite.com/dopage.php?p=mypage.html

....and then the php could do some fancier includes at the end of each page,
etc., or add a header, etc.

I don't want to rewrite the whole site and rename all the pages; also, this
site has been around for awhile and there are a lot of links floating around
the internet to direct urls on the site, so I'm wondering if I can intercept
every URL to that site and redirect it to the php function, which will then
open the page.

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