I have both the Citi aadvantage Amex & visa personals from 2BM since Nov 2011.
Have the Citi Aadvantage visa biz since 2012. Got the Citi Aadvantage mastercard in July 2013.

Do I have a chance to get this executive aadvantage card now? Or chances are slim since I have 4 addvantage cards already?

In addition to the above, I have the 2 Citi Hilton honors card since early 2013 I think & the dividend mastercard since 2010.

Should I close one first and than apply for the new offer next day?

My wife has about the same citi cards & unlike before, she got rejected for citi aadvantage biz mastercard. They said she already has citi biz card.