Yes, you can activate another phone on your line. Just turn off the current phone and dial *228 and choose option 1 from the new phone. The new phone must be Verizon branded and have a clean ESN. If you need to buy one, you can pay full retail through Verizon (unless you are eligible for an upgrade), or get one used from eBay or another source. If you do buy used, call CS before you pay to confirm that the phone can be used with your plan and has a clean ESN.
Thank you SpottedCatfish for providing very good information on how to switch out a phone.
Below is some additional information that might prove helpful.
You have the following options for activating a different Verizon Wireless device on your number:
1. Dial *228 (Send) and press option 1, when prompted, from the device you want to activate and listen for further instructions. Please ensure the wireless device you wish to deactivate is powered off.
2. Sign in to “My Verizon” using your Account Owner user ID and password and click “Activate a Device” icon located under “Device” in the “I Want To” section of your home page.