If you have a desktop that has an extra drive bay available, then yes, you can.
Shut down the computer and unplug it.
Open the case and locate your current hard drive. It's normally near the front of the computer, and there should be some other empty bays. Normally you'll just slide the drive in, use some screws to hold it in place, and the plug in the power and SATA cables. There should be an extra hard drive power cable in the case already although you'll probably have to go buy a new SATA cable from a computer parts store. Make sure you get one that's long enough to reach the SATA ports on the mother board.
Once you've installed the new hard drive, seal up the case, plug it in and power on the computer. If the drive wasn't already formatted, it won't show up in the File Explorer yet. You'll need to run the Drive Tool to format it. A quick format should be fine.
Now that drive is formatted it'll show up in the File Explorer, probably as E:\
If you want, you can migrate your Steam directory over to E:\ This will move your current games over.
You can make E:\ your default location for Steam, or you can simply choose where to install new games.