If youre not looking for anything offshore/anonymous etc, you can open Mercury.io as a foreign non resident, you just need an LLC which you can also form online for cheap.
You do not need an ITIN, and it is completely online. They are pretty easy to get, I have one, just upload docs and wait a week.
Youll get a Debit card, can send/receive ACH/Wire/International wire, they just added virtual cards as well.
Also free to open.
Can deposit and send checks as well which you cant do with EMI to my knowledge.