Approval Process or Build Custom Flow for Approval Process on a case

I need an approval process that requires:

• Multiple approvers
• Multiple step process

eg  Case is created  -->  Request Approval  -->  Approver 1  -->  Approver 2  -->  Manual update to external system  -->  Manually send email(s)

There will be rejections that will require more information before going back to Approver 1.

I'm looking for opinions, pros, cons as well and suggestion on modeling.  

• Salesforce out of the box Approval Process
• Custom Flow
• Something completely different

Thank you in advance for your input and assistance.  I look forward to your responses.