I am trying to allow a responder to add an additional field if necessary. For example if they are listing the residents of their household is it possible to insert an 'add' button so that a second, third, fourth etc. field is created but is not automatically there?
You can use Skip logic (Show/Hide) to expose additional questions when one question is answered in a specific way: https://www.acrobat.com/formscentral/en/library/skip.html
Show/Hide logic is a feature in a Paid subscriptio to FormsCentral.
You would add all additional questions in the Design tab authoring the form and would set questions "Show/Hide" logic to only show them when another question such as a Single Checkbox for "Add additional person" is selected.