How can a respondent save a JotForm half way through and have another person contribute to the form?

Based on the requirements you have mentioned, I believe what you would like to set up is similar to an approval process workflow.

And to set up a form with that workflow, may I suggest that you refer to this user guide, please?

A-General-Approach-on-Building-an-Approval-Process-Workflow

Please give it a try and let us know if you need any further assistance.