Is there a way to send a partially filled out form to a customer so they can fill out the rest?

Is there a way to partially fill out a form and send the partially filled out form to a customer so they can fill out the rest and submit it?

For example, our form is a customer contract, and we want to be able to customize the completion date for each customer, because it is specific to each one.

Yes, that's possible by prepopulating the form fields using URL parameters.

Here's how: http://www.jotform.com/help/71-Prepopulating-the-fields-to-your-JotForm-via-URL-parameters

Then all you have to do is to share them the form URL with the URL parameters.

Example:

https://form.jotform.com/61864660544158?selectThe45=Deck%20Staining,Pressure%20Washing&name[first]=John&name[last]=Doe

This selects Deck Staining and Pressure Washing options with John Doe as the name.