U.S. / E.U. business structure - payments & billing flowing through a third party company?

[Cashimir]

For context - I operate a business (shopify store) that is registered in the E.U. where I live with 90%+ of my revenue made from the U.S. Is it possible for me to register my Shopify store to a U.S. LLC while having invoices made in the name of and payouts (from Stripe, Shop Pay, Paypal) made to a E.U. company?

The reason I'm asking is that there are a lot of services and critically important Shopify functions that are only available in particular geographic regions, such as Shop Pay, buy now pay later services, Tiktok stores etc. I'd like to make use of these services, but for the time being it simply isn't an option due to where my business is incorporated. So my question is as follows: if I were to register a U.S. Company, would it be possible to register my store to this company, while keeping both billing and payouts moving through my E.U. company?

Having to move my entire operation to a U.S. based company would incur various operational expenses and obligations (having to navigate the US tax system etc) that might be a considerable entry barrier for me, but if I were to be able to be able to use the U.S. company as a local "representative entity" for US services that require it while keeping accounting E.U. based would simplicate matters a lot.