How can I create duplicate student fields that are contingent upon someone answering "Yes, I would like to add another student"

I'm creating a counselor recommendation form, and I need to create a way for counselors to select an option to add additional students after they enter the requested student data  Is there a way to do this on jotform?  

You will need to create the set of fields per student and show them  based on conditions, here are some links that will help you doing so: 

https://www.jotform.com/help/297-Show-or-Hide-Multiple-Fields-at-Once-Using-the-Section-Collapse-Field

https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

If you just need to ask basic data such as name, email, date of birth, phone number, you may use any of the multiple entries widget found here: https://widgets.jotform.com/category/multiple_entries 

This guide will help you adding the widget to your form: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-Your-Form 

I hope this helps.