Can a survey respondent add sections as needed?

For example, I would like users to be able to list an educational institution they attended, and have the option to add another if there's more than one.

That would depend on the type of the field you are looking for, but cased on what you have mentioned I presume that you need a text field.

To do that I would recommend using our Infinite list widget.

You can see here how to add it to your jotform: How to Add a Widget to your Form

Do let us know if that is what you were looking for and if you have any further questions and we would be happy to assist.