Enrico, 

You can accomplish this by making a copy of your original form and give it a name like "Supervisor Approval Form".  Then use this form for the approval process and it will contain the information from the original form.  You can add needed additional fields to this form (note, these added fields will not be added to your original form unless you manually add them) for the supervisor approval step.  In the Business Process for the approval step, you can assign the new form to be used for that approval and also mark the form as read only if all the approver needs to do is review the form and then click an approval button, but if the approver needs to enter info into fields you added, I would set all the fields from the original form as read-only so they can't be changed and keep the fields "open" for the approver that they need to fill out. 

If there is another approver process and you need additional fields, then repeat the copy process for another form (your finance form) and name it accordingly and add the needed fields for finance to complete.  Make sure to have the finance approver process use this form. 

When everything is completed, and it is time to save to Laserfiche, use the latest form to save to Laserfiche and it will have all the information gathered across the processes.

To make a copy of a form, have the form you want copied selected and then select the copy icon in the upper right.