If you believe the Single European Market propaganda, you would be right to believe that a company incorporated in any EU state can undertake work in any other EU state - in which case LUX (or EI, NL) may be the answer to your question.

However, the SEM is rarely straightforward in practice, and I know from first hand experience that using your own contractor company in Germany (even if incorporated in DE) is quite tricky as you have to comply with the various labour laws. This can make it non-viable, and most contractors end up working via management companies.

In terms of tax, there is a major difference between tax residence and tax domicile - so even if you register your company (domicile) in (eg) LUX it may be resident in multiple countries simultaneously.

You need to take proper legal advice...

If you believe the Single European Market propaganda, you would be right to believe that a company incorporated in any EU state can undertake work in any other EU state - in which case LUX (or EI, NL) may be the answer to your question.

However, the SEM is rarely straightforward in practice, and I know from first hand experience that using your own contractor company in Germany (even if incorporated in DE, never mind LUX) is quite tricky as you have to comply with the various labour laws. This can make it non-viable, and most contractors end up working via management companies.

In terms of tax, there is a major difference between tax residence and tax domicile - so even if you register your company (domicile) in (eg) LUX it may be resident in multiple countries simultaneously.

You need to take proper legal advice...