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Currently have a Chase Slate with 0% til Dec 2015 and 7K CLI... Is it advisable to also apply for a Chase Freedom....
Yes it is possible. However, it appears Chase has revisited it's approval guidelines and some are having a tougher time opening additional trade lines if they've opened too many new accounts recently. There is a whole thread about it, just search for it.
Also, you may get more hits on this question in the regular credit card section rather than in the approvals section.
OP- you can definitely have both chase freedom and slate. I have 7 chase cards, they do not limit you on cards but instead your exposure with them.
Im sure you can.
I got approved for Freedom and Slate one day apart and with only one HP! Im pretty stoked!