with Maßen as an old genitive or in a dative-for-genitive situation and as a whole being an adverbial genitive [cp. www.dwds.de/wb/einigermaßen : "einigermaßen Adv. [...] anfangs (17. Jh.) in genitivischer Fügung einiger Maße" though this expression seems to be uncommon], or
with Maßen being an old adverbial dative (pl. - though historically, it could possibly be sg.) with sense "with some extent[s]", cp. with allenthalben in locative sense "on all sides" meaning everywhere?”