Add another item by multivalued fields directly from node (or entity) view page
You can able to achieve it using Edit module which supports D7 and file Entities...

Project page says


  In-place editing for fields on any entity. Including WYSIWYG editing
  powered by CKEditor.
  
  In-place editing through forms will work for any field. For textual
  fields, "direct" editing is used, powered by contentEditable.


Here is the sample screenshot which shows inline editing of Multiple File Field.. Here is how i can able to achieve it..


Install like any other Drupal module.
Download Underscore 1.5.x and Backbone 1.x from http://underscorejs.org/ and
http://backbonejs.org/, respectively and put them in sites/all/libraries, in
a "underscore" and a "backbone" subdirectory, respectively. Either the
development or production version will work. Edit module will automatically
use the production (minified) version if it's available, because it's more
efficient.
Grant the 'Access in-place editing' permission to relevant roles.
Contextual links on nodes will now have a 'Quick edit' link. Clicking it will
start in-place editing of that node!




Seems like editablefields module also provides same functionality..