I don't carry books around; I read whatever book I have at hand.
I have a book by my bed at home, a book for the rest of the house (that I also take with me to the kids' practices), a book that I read at work during lunch, and a book on my phone (when I am away from all the other devices; it is my least favorite way to read). Sometimes I have an audiobook that I listen to on my drive home from work.
So, yes, I read multiple books at once. I think I have five going right now.