Again, with the disclaimer that every single profile is different and can yield different results:
I’ve opened 13 accounts since 2/2018. Five of those are Amex. When I cold apped my first time for Amex in November, it was for Delta Gold and Hilton Honors. I did them 90 minutes apart and was approved for both. My next one was the Hilton Ascend on 3/3, followed by BCP on 5/23 and Gold on 5/27. All were approved, even with two of the other new cards happening in among the Amex apps.
I am sure that any lender has a point where they say enough is enough. I found that in my case, they were quite generous with card approvals and the other accounts I had opened did not seem to bother them much. But I can’t stress enough that YMMV. Among cards I’d had before 2/2018, one is 5-1/2 years old, one is 13 years old, and as of that date I had three old, closed with perfect history car loans on my EX, all of which I’m sure helped when added to my newer account histories (all of which also have perfect payment records).
Your score will matter with Amex but I am willing to say that the overall picture of your credit history will matter just as much.
