Yes you can.
Depending on the type of pineapple you have (Ananas comosus blah blah blah) some readily make offsets (pups) and some don't. You can always wait til your fruit is ripe, cut it off, eat the fruit and save the top and plant it, and get a new plant. But look around the base of the plant also to see if you are getting offsets forming. ALso, on some types, new offsets will form on the stem with the fruit.