This seems like potentially an extremely expansive power. Especially since most companies regularly infringe regulations of various sorts at one time or another.
Could a company (e.g. the Trump Organization) be hauled up if it were suspected to be selling, to EU nationals, packages comprising both a hotel room and (say) a tour of the White House or some other non-ancillary tourist service without complying with Directive 90/314/EEC (http://eur-lex.europa.eu/legal-content/EN/TXT/?qid=1432309131133&uri=CELEX:31990L0314)? Presumably the New York courts wouldn’t be able to get a preliminary ruling on for example what counts as “other tourist services not ancillary to transport or accommodation and accounting for a significant proportion of the package”.
I just don’t think that Quo Warranto is intended to be used in that way.