Welcome to FT djmatthews.

You can get a second card but I wouldn't apply straight after you got the classic, if that's what you were going to do. I had the classic and applied for the Premium/Platinum. They knocked me back at first so I called and told them I wanted to earn 2 miles per pound instead of 1.5. They agreed to take the credit off the exisiting card and transfer it to the new one and treat it as a new application so I got the second 20K.

I can't commment on what it does to your credit rating !.