We do have some existing ticketing plugins which could effectively serve this purpose – Eventbrite Tickets and WooCommerce Tickets – and may be adding more over time.
Beyond that you’d have to consider a custom solution.
Thanks. I’ll look into the Ticketing add-ons. Looks like a new one announced today. All of them may be way more than I need for my small office.
I suppose I could roll up my sleeves and try to make my own Gravity Forms solution for simple signups.