[funkymusic]

In this case you could do a so-called flip bringing your assets from the EU to the US (contributing cash and assets).

A drawback is everything depends on the main E2 visa holders - as long as this person holds the visa others can follow; if this person does not hold the visa any more, all attached immigration permits are gone as well (e.g. if the company goes out of business you can't stay in the US and look for a job).

[filip01]

Great, thanks. Do you know of a more formal way of expressing this "flip"? (Don't get any good Google hits).

[shimms]

It generally is referred to a scrip for scrip rollover (terms may vary based on your country of jurisdiction).

You're essentially swapping your ownership in the foreign company for the equivalent ownership in a US company, and the US company becomes the sole shareholder of the foreign company.