Allowing users to add additional fields

You can use the dynamic widgets for this.

You can check them here http://widgets.jotform.com/category/multiple_entries

Example

1. Dynamic Textbox

2. Matrix Dynamique

3. Configurable Lists

Here's a demo form to check http://form.jotformpro.com/form/51233651283955?

Let us know if you need further assistance.

Thanks.