I saw this a lot when I ran BD for the program (I'm also an American) and its good you know there will be US tax complications but I would say that unless you expect to 1) have many EU customers and 2) working remotely globally and redomicile elsewhere so you are not considered US tax resident that it probably doesn't make more sense than using something like Stripe Atlas to just set up an LLC or C-Corp
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I saw this a lot when I ran BD for the program (I'm also an American) and its good you know there will be US tax complications but I would say that unless you expect to 1) have many EU customers and 2) working remotely globally and redomicile elsewhere so you are not considered US tax resident that it probably doesn't make more sense than using something like Stripe Atlas to just set up an LLC or C-Corp
The point is serving EU customers as a EU company yes.