You can create a custom form to collect data from people when they buy a membership plan.
Follow these steps to setup the form:
Login > Groups > Click on "Manage" button > You land on Overview page > Group Setup > Membership Form

On this page you can Enable the form. Once enabled, you can also opt to have different forms for different membership types.

Choose from the available field types like Input, Number, Select Menu, Date, etc and drag it to the Form Designer area. 

Click on the Action button next to the field and add the Label name. You will have to provide options for Select Menu, Multiple Choice and Radio Button. You can drag and drop the fields to set the order of the form.

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