can i upgrade a 16GB IPad 4 to 32GB after purchase?

If you mean upgrading the iPad then no, it's a sealed unit and its capacity can't be changed. If you bought the iPad from Apple within the past 14 days then you could take it back for a refund and buy the 32 gig version instead. Otherwise there are some wifi-enabled external drives that allow you to stream content to the iPad, so you don't have to store your music, films or tv shows on the actual iPad.

re K-Ps suggestion have a look at airstash a quite flexible solution