Unfortunately you will not be able to open another slate card. You may be able to open a freedom card, but it will be a 3% balance transfer fee. I have not heard of anyone product changing a freedom to slate, but I have the other way so you may be able to get away with that (giving if they have a visa and MasterCard slate).

I was talking with Chase yesterday and they said their system will now automatically deny someone who's been approved for the same card. I was trying to get two CSP (mc and visa).