Had been waiting for a paid balance transfer to finally reflect on my reports and discovered that it did today. So I decided to apply for three cards that I had been eyeing (Chase Sapphire Preferred, Amex Blue Cash Preferred and Discover IT) and then, on a whim, decided to apply for the Amazon Prime Card.
Ended up getting approved for all four! CSP - $35,000; BCP: $25,000; IT: $24,500; Amazon: $3,000.
From what I've read lately, it seems that a few of these cards hand out a CLI at activation. Given that my initial limits are so high, is an instant CLI still likely?
Whatta nice haul all in a roll! 
Congrats!
Thank you 
It was very exciting to see all of those approvals in a row. I usually only apply for 1 card every couple years but decided to just go all in this time!
Thanks everyone
So UPDATE - I called Credit Solutions because I felt the $3,000 limit on the Amazon Prime card was a little low. She asked what I would like to request, so I threw out $15,000. I expected her to deny and then counter with something like $8,000 or $10,000, but she granted me the full $15,000! I guess I should have asked for more .