See https://www.mediawiki.org/wiki/Parsoid/OutputTransform; this is step 3 and 4 of the "initial proposal":

3. Add ParserOption::get/setFlavor() (not included in cache key), and add support in ParserOutputAccess::getCachedParserOutput() to check the flavor and if it's is not core, to call MediaWiki\ParserOutputTransform\FlavorDispatcher::transform($parserOutput, $parserOptions::getFlavor()). It will also consult MW config and a hook to determine whether or not to cache the result.
4. Add a hook in FlavorDispatcher to allow inserting additional passes into the chain for any flavor; this will replace the ParserOutputAfterTidy hook.