Just got approved for my 2nd US Amex (green card) and you have to hold your nerve and have the information at hand.
Applied online using Amex US login and got the "We need more information" and please call. So I called up and he asks the normal address and phone number questions and then says we can't verify SSN (I used ITIN) so can we call your bank to verify. So we do a 3 way call to Capital One and he asks the same questions and verifies address, phone number and SSN (ITIN) and finally all approved but nerve racking and I have my PostScanMail address up and my ITIN number, textplus number and paranoid so the weather and time in Long Beach haha (smokey and 23 degrees)
Another issue was they couldn't verify my phone number belongs to me but got past that with ITIN verification. I did order that T-mobile sim card as I see this being an issue with Chase and Citi.