Most banks will allow you to have multiple cards as long as they are different. Such as one being a rewards card, another cash back, airlines card, master card, visa, ect. But you might get smaller and smaller credit limits on each new card. You can move credit limits between cards at will by calling the CSRs. So even if you get a small CL you can share from a higher one. Some banks have a restriction of lets say 90 days before you can apply for another. I don't believe Chase has any restriction on app dates. You will get separate inqs for each app even if done the same day as in my case. But you never know.
