Not sure others posting answer are correct here. Yes, Citi AA Plat personal is different than Citi AA Plat biz, so you can get both cards approved and hold both at the same time.

BUT they both give AA miles as bonus for meeting min spend, and both give the same family of points (AA miles). Citi's new rules say no bonus points for meeting min spend if you've had same family of bonus-by-meeting-spend points in the past 24 months.

So, yes you can get the biz card even though you have the personal card. But no, you won't get the 60K-ish AA bonus miles for meeting spend if you've received other AA bonus miles for meeting spend in the last 24 months.

Well, not unless you have one of those 9 digit mailers that have no 24-month language on them.

P.S. Just googled OMAAT article and they agree: "Unfortunately Citi added a further restriction last year, as you’re not eligible for the bonus on a card if you’ve had the same “type” of card in the past 24 months. For example:

The Citi® Hilton HHonors Reserve Card and Citi® Hilton HHonors™ Visa Signature® Card qualify as the same “type” of card The Citi Prestige® Card and Citi ThankYou® Premier Card qualify as the same “type” of card The Citi® / AAdvantage® Executive World Elite™ Mastercard® and Citi® / AAdvantage® Platinum Select® World Elite™ Mastercard® qualify as the same “type” of card"