From the backend, your base would be setup with both an application table & a teammates table. Then, you would link the 2 tables together: each application in the application table would be linked to several teammates in the teammate table.
However, Airtable does not allow creation of linked records via a form.
So you would likely need to turn to external automations & integrations to handle this. If you could find a form software (Gravity Forms? Formstack? JotForm?) that supports handling multiple applicants in the way that you need, then I’m assuming that you could automate the procedure of getting that submitted data into the appropriate places in Airtable using Integromat or Zapier.
It’s possible that someone else might have some other ideas for you as well!