Hi Casey,
You may have already done this; check your Signature tab in the Object panel and ensure your fields do not have 'lock fields after signing' selected. It is selected by default when you add a signature field.
You can use this tab to have each signature field lock a selection of fields, all fields, or no fields.
Also, depending on your form, it may be worthwhile to save it as a 'Static' rather than 'Dynamic' form; in my experience, this seems to help multiple signature fields run smoothly, although it does limit other functionalities in the form.