Like lots of other people I always had a hard time getting the third card of a Chase 3bm approved, but here is what happennd last week.
my wife applied for the Sapphire card in a Chase branch got instantly approved, a few hours later we did a 2bm for BA and UA from home both were pending so she called reconsideration right away and they approved her for both cards in one phone call, here is the beauty the rep didnt see the application of the just approved Sapphire in the system!! maybe when doing a AOR this is not a good idea but when you wonna do just a Chase 3bm maybe this is the trick.... applying for the first one in the branch, then do a 2bm, call in reconsideration and they will not see your first approved card.
Of course YMMV however it worked for me so it does not hurt to try.
Good luck!!