It seems to be a total YMMV thing, but at least anecdotally, once people have more than 6 personal cards they start to run into resistance from Chase about having too many cards.
I currently have 2 with Chase, both instant approvals. I think I've read on the forum that it was 4-6, but I'm planning to go for one more Chase card (Marriott) and then that is it for now. If need be, I might have to move CL if I am approved in the future, but I'm not apping for 6 months so I have some time to decide whether I will app for it when the time comes.
Another data point here. 3 instant approvals in 4 months.