What action or filter can I use to change all the html returned from server for a page?

If i understand, You simply want to have all html from page. Why just don’t do a request to the page in response You have html.

Here is the suggestion from codex:

/** @var array|WP_Error $response */
$response = wp_remote_get( 'http://www.example.com/index.html' );

if ( is_array( $response ) && ! is_wp_error( $response ) ) {
    $headers = $response['headers']; // array of http header lines
    $body    = $response['body']; // use the content
}