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Well, all 3 might pull different CBs anyway but 3 inquiries is really not a lot...especially on different CBs.
I would venture to guess AMEX and Discover will likely pull different bureaus but you never know. I need cards too - I just got 3 together. I was able to get 2 AMEX for 1 HP on EX and was able to go for Discover which fell on EQ. So, that was my strategy. But, it's still 3 new accounts.