My slots are filled by:
Blue Cash Everyday (opened 3/14)--$250 sign-up bonus
Old Blue Cash (9/14)
No Annual Fee Hilton (12/14)--60K point bonus
I just cancelled a little-used Amex Blue (2/08) last week, so no MR cards. I maxed out the BCE CB this year and last; the last CB will post in April. I'll apply for Blue Cash Preferred in April (a better CB return than BCE even with the annual fee since I know I'll max out the $6K) and cancel the BCE if that's approved. These are the only Amex cards I've had. I plan to keep the OBC and BCP long-term, but not the Hilton card.
In my dreams, removing the Blue and not applying for the Everyday MR cards will increase the chance of a 100K MR Platinum or other huge offer (I know the Platinum won't take up a slot). With the one bonus per lifetime rule in addition to the 4 slot rule, I'm weighing my options carefully before deciding to apply for any other Amex cards.