A little bit of background:

I am a college student, with my credit score in the low 700s. Not having a ton of credit history, I'm a bit limited when it comes to the churning game.

Anyway, I'd like to get the Chase Sapphire preferred card. I'll meet the $3K spend no issue. However, I only have one other Chase card (UA Explorer) with a small limit. I plan on dumping the UA card in order for the Sapphire card.

Here's the dilemma: should I cancel the UA card, then apply for the Sapphire card? I feel that Chase won't give me a second card due to the fact that I have a limited credit limit with the UA card now. Should I take some other strategy?

For what it's worth, I also have two AMEXs: one charge and the other the SPG card. Any help appreciated!