I doubt it, dunno why they would, but just ask them I mean they won't be like "well we would have given you a second one but since you brought it to our attention and asked NO DEFINITELY NOT FOR YOU!!"
Fwiw: chase lets you have two 0% offers concurrently, but will not let you open a card that you already have (Ie you can't open a freedom if you already have a freedom [although having a Freedom won't stop you from PCing another card to a Freedom thus giving you a second one]). US Bank though will definitely let you open a second Cash+ if you already have one, in fact when I asked the rep about it over the phone they seemed rather encouraging of the idea. So I expect us bank won't have any issues with you having a second 0% offer.
