Why not use the existing drop-down menu  and expand that? You can add
and remove content on that menu using a CustomAction feature  as
described in my article at SharePoint Magazine:
sharepointmagazine.net/.../customizing-user-
experience-sharepoint-modifying-default-experience-part-2-6

If you want to add  your own column you should be prepared for some
development work, either by making your own field type to house more
complex logic or by creating your own view schema code.

You wouldn't add  this functionality  bye editing the AllItems.aspx. You would
add it by creating a custom column and adding it to the list. The grid you see
on the allitems.aspx page  is a list  view web part and can't be edited directly.
You could replace that with a DataView web part, but the columns there still
come from the list you are displaying.