Those with four INK cards had an 0% chance of getting approved for an INK card. 
Applied for a second ink since the Unlimited pays 1.5% uncategorized while my preferred only pays 1% uncategorized. Didn't really wnat a second card, but also don't feel like leaving money on the table. It's always a ridiculous process with Chase for me as they have my info on some type of fraud alert list where I have to send in verification docs, or go into the branch to prove my indentity, every time I want to open a new checking account or credit card with them. I've had to speak to about 7 foreign call center reps so far, and now this second application seems like it's finally going through but just very slowly as usual (was able to see the APR of ~17% I guess it's approved), but now I've noticed that it no longer shows me the option to apply for additional Chase Ink cards when I'm logged in - it just shows me the southwest and united business cards. Before this app it showed me 3 Ink options as well. Maybe 2 Ink Cards is going to be the new limit.
