Hi Matt,
You will need to create a new Phone Button Template (maybe called 7960 - 6 Line) as described below. Once you have created the new template you can assign it to the phone in question Device>Phone>Button Template>7960-6 Line>Reset and you will see that you have the ability to add 6 lines;
Adding Phone Button Templates
Step 1 Choose Device > Device Settings > Phone Button Template.
The Find and List Phone Button Templates window displays.
Step 2 In the upper, right corner of the window, click the Add a New Phone Button Template link.
The Phone Button Template Configuration window displays.
Step 3 From the Phone Button Template drop-down list box, choose a template and click Copy to create a new template.
The new template exactly duplicates the existing template. You must assign a new name for the new template. Update this new template if you want it to differ from the original.
Step 4 Update the appropriate settings as described below.
Step 5 Click Insert to add the new template.
Step 6 Click the View Button Layout link to verify the button layout.
Phone Button Configuration Settings
Button Template Name
Enter a unique name that Cisco CallManager uses to identify the template.
Feature
Choose the function of the phone button that you want to specify in the template. Available functions include Speed Dial, Line, None, Privacy, and Service URL.
Note You cannot change the function of buttons in default phone button templates.
Label
Enter a description of the button.
From this good doc;
http://www.cisco.com/en/US/products/sw/voicesw/ps556/products_administration_guide_chapter09186a00803ed6f4.html#wp1014156
Hope this helps!
Rob
EDIT: Matthew and Chris you are too fast on the draw for this lame-o typist :)
