Can i download a new iTunes and keep old one

hey! :) ok so i have a question... can i download a new iTunes and keep the old one that i have?...cause i have had my iTunes account for like 2 years and i just bought a new ipod and gave my old one to my mom! I was hoping there would be a way that i could keep my old one for me and download a new one for my mom and have them both on the same computer, so that way our muica will not have to be 2gether! Can this be done is the question!?