I once got approved for five Bank of America credit cards in one sitting (one Alaska card, two Virgin Atlantic cards, and two of
those random bank rewards cards offered by Bofa), so you may be able to get more than two at once.
Not exact matches
US
Bank does offer quite a few travel
rewards credit cards like their Flexperks
rewards program, and they offer few
random (but useful!)
As I said, I had one card with a
random local
bank and then got my first
rewards card with Chase.