If you have PHP code generating the page, you could use the output buffer to generate the page in memory, edit the generated page and then flush it to the browser. You can only change the DOM before the browser gets it.
You could do the following:
ob_start(); // Should be called before any output is generated
// ... PHP code that outputs HTML ...
$generated_html = ob_get_clean(); // Store generated HTML to string
// Load and manipulate HTML
$doc = new DOMDocument();
$doc->loadHTML($generated_html);
// ... Manipulate the generated HTML ...
echo $doc->saveHTML(); // echo the modified HTML
However, since you are generating the HTML it would make more sense to change whatever you need to change before it's generated to reduce procesing time.
If you want to change the HTML of a page which is already shown in the browser you'll need another way (such as JS/AJAX) since at that point PHP can't possibly access the DOM.
DOMDocument, or any other tool within PHP have the capability of parsing local DOM elements?