Process help for fillable form, multiple signatures, print to pdf

I'm new to this for a new job so trying to understand what is the best process for our needs.

Basically this is a form with multiple sections and multiple people will fill/date/sign in a particular order as tasks are completed.  It is emailed/downloaded/saved multiple times.

Is there a way to do this without person 2 needing to "Print to pdf" and needing to "prepare form" 

to be able to add in new check/text/date/signature boxes overtop of what is already there to be able to fill them in and sign. (it seems redundent to need to prepare the form when it already had those fillable sections in the original document) I understand this is due to security for the signatures, but since this isn't a legal document, its not super important for us, but we do need the multiple signatures, so wondering if there is something I am missing, or if this really is the only way?

Here is an overview of what I'd like to do without person 2 needing to prepare the document again.

• Fillable form sent to Person one - (downloaded from a website)
  • They fill in the top section and digitally sign
  • Emailed to Person 2
• Person 2
  • Download to desktop
  • Fill in second section and sign
  • move to a new folder
  • Form emailed to person 3
• Person 3
  • Downloads and signs section 3
  • save and email back to person 2
• Person 2
  • downloads form to desktop
  • On some forms Person 2 will need to fill out section 4 (unlikely to need to sign this section)

I'm not sure if I explained myself good enough - but I appreciate any guidence.

Thank you!