Unfortunately Airtable forms don’t have that kind of flexibility. Part of me feels it would be a useful feature, but letting any user add a choice to a Single- or Multi-Select field from the form level opens a potential can of worms.

I feel it would be preferable to add a text-entry field adjacent to the drop-down with a label like “Don’t see what you want in the list above? Add your preference/request here:”. That allows someone to monitor those requests and only add those items to the drop-down that a) aren’t pure nonsense, and b) are truly worthwhile options to add.