Not a useful answer I'm sure, but I definitely think it depends on your preferences, shopping habits, and priorities. Do you shop at the stores that are specific to the store cards? Do you get useful benefits/discounts/rewards from them? Do you carry a balancer or PIF (thus determining whether APR is a consideration)? Are you concerned with utilization and credit limits? How difficult is it for you to responsibily manage all these cards? Are any of the cards costing you money in the form of AFs and fees that you're not recouping through rewards (and wouldn't be able match with a less expensive option)?
In general a lot of people will probably say close the store cards and keep the major cards, but it's not always that black and white. Personally, I have one store card, my Target Red Card, which I absolutely love and get phenomenal value from. I have several major network rewards cards I'd close before I'd be willing to close my Target card.
If we're talking personal preference, I'd keep the Discover It and Chase Freedom, because I do in fact have those two cards and really love them. I'd personally be A-OK with closing everything else, including the CSP which I also have but intend to close myself, because I wouldn't/don't personally get much value from them. LOL, but of course my preferences, spending habits, and priorities are almost certainly much different from yours.
