Sorry it's taken me a day to get back to you, I've been pretty busy...
I don't know if I understand what you're wanting to do or not, but the only way that I'm aware of to put multiple "IF" statements into one field is to do it the way I demonstrated above. You can put as many as you'd like in there to achieve what you're trying to do.
This is just a shot in the dark, but I've re-read your posts several times now and am wondering if it would work the way you want if you change the formula in A2 to something like this:
=IF(A1>DATEVALUE("5/31/2014"),"GOOD",IF(A1>DATEVALUE("6/31/2014"),IF(A1>DATEVALUE("5/31/2014"),"EXPIRED","EXPIRING SOON"),"EXPIRING SOON"))
I really think you will need to play with the formula above to make it work, but I think something like this is going to be your best bet.
Law of Logical Argument: Anything is possible if you don't know what you're talking about.