I’ve been approved for the following cards with two to three unpaid collections and a sub-700 score:
-Amex Every Day $4K SL (7-10 day message, immediate recon - April 2018)
-Amex Blue Cash EveryDay $4K SL (immediate approval same day after other Amex approval - April 2018)
-Barclays Uber Visa $500 SL (7-10 day message, recon - May 2018)
-Capital One Platinum $500 SL (immediate approval - December 2017, PC to Quicksilver in April)
Discover It $1.8K SL (preapproval offer via mail, immediate approval - December 2018)
That is every single credit card I currently own. I canceled my only previous card two months ago, a Credit One that I had since October 2016.
Keep in mind, however, that two of the three collections in question were medical and five to six years old. The other was originally a 2011 Cap One chargeoff that went to Portfolio Recovery and has since fallen off, although they continue to call me from a different number several times a week and I never pick up.
FYI, I still have an open medical collection on TU, and two on both EQ and EX. In spite of this, Capital One has increased my limit to $1,100 (2 CLI), Discover has increased my limit to $2,900 (3 CLI), and the Amex cards now sit at $10k and $5k (one CLI) after a relocation of limits.
I hope that helps!