You can! A foreign EU company just needs to get a "Betriebsnummer" (company number) from "Bundesagentur für Arbeit", which doesn't even require a Betriebsstätte (permanent business establishment, a branch that is not legally independent) or a "Zweigniederlassung" (branch office, legally semi-independent, but still part of the same entity) - and certainly not a subsidiary that has it's own legal persona.