I have:
Freedom
Amazon
ToysRUs
SW Premier Personal (converted from some other personal Chase card)
SW Premier Business
Ink+ (Got this last month)
So I have 4 personal, 2 biz. For the SW personal card, they said I had too much credit and would only offer me the card if I closed an account. I applied for both SW cards the same day and both required a call to the recon line.