You can add an additional DataSource for submission (send to SharePoint library) and add a rule to your submit button before the save&close rules.
BUT - I would suggest a method that is based on workflows and a form that is held on a SharePoint site. I had a very similar task, where approvals were needed in a staged manner.
If there is a fixed number of approvers, create fields for each one - if the number is not fixed you will need some replacing rules that change the current approver with the next one. Then you will need one (or more) workflows that are triggered by a flag field (or more) that you promoted before. (Make them writable from the outside during publication - the workflow will need that) This field (or fields) trigger the workflow that sends the email. After sending it should clear that flag to avoid infinite looping.
The mail should contain a link to the SharePoint library. And the approver should work on that library rather than sending the XML file through the network.
Hint: Enable versioning on that libary - and you (or the approvers) can keep track of the changes.
Hint 2: If this process will be part of the daily work, maybe a custom view and alerts will help the approvers keep track of the form's status.