Sure. If you have windows it's best only to run one at a time, but you can have as many versions as are compatible with your operating system.
Thanks, Barbara...I have version 9 and 10 installed and when I load photos into the computer they always end up on version 9. I am flumaxed.
Turn it off, and then the next time you plug in your camera or card reader, you can select PSE 10 downloader in the windows system window that appears.