I looked into GmbH (german) , BV (dutch) , and OU (estonian) . GmbH seems very unpleasant. BV and OU are easier to obtain. But BV requires your primary place of business to be the Netherlands, which isn't always practical when you're trying to extend your activities internationally. OU is supposed to be better for international operations, but -because it's a single country initiative- creates new and interesting tax problems.
At this time, the whole system seems to revolve around geographic location. As long as you stay put you're sort of fine, but if you move around within the EU, the law doesn't stay stable around you. This is impractical.
EU Inc seems to be a new initiative to fix a lot of the patchwork problems, but doesn't seem to be live yet. ( https://commission.europa.eu/topics/business-and-industry/do... )
I'm told that interstate commerce in the US isn't always necessarily easier, mind. Maybe the EU can take some lessons learned.