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I've had these Capitalone Cards since 2007/2008 and they haven't grown at all since then. One increase in 7 years, limits of $750 each, I've tried the EO and nothing from them. In total I had 5 Capitalone cards, the Venture with no fee, a playstaion rewards, two quicksilver cards, and another quicksilver that was a hsbc account. I've wanted to try for another Quicksilver or Venture card, but I kept getting declined for having too many accounts with Capitalone, so now that I've closed these two, maybe I'll get another card with a higher limit. My current venture is $3500, and my scores have improved since getting that card.
I'm going to wait 30/60 days before applying though.
The maximum CAP 1 cards you can have is 5. So closing a few will certainly help your quest in applying for a new one. If I were in your shoes, I'd wait 90 -180 days before applying for another card.
If you already have 5, closed 2 then give it some time beofre applying after getting denied so many times..
I closed a Prestige(?) MC with a $3k CL early Feb, got another QS Sig middle of April, roughly 75 days, $5K CL. I just closed a QS1 $3.5K CL last week. Now have 4 cards, total CL $40.5K.
Awaiting a decent CLI offer on my Venture, I've been withdrawing the $2K offer. 75 days after opening or closing seems to be the "magic number"