How about if you used a drawer-type interface (from material design) for the references, with a modal for the activity of emailing it to yourself, or sharing it on social media?
In the main layer, the user is presented with the text of the article. When they hover over the reference number in the text, they get a popup with the details of the reference, and a button saying "save reference".
In the drawer layer, accessed by clicking on the hamburger icon at top left, they get to see their list of saved references (this could also have buttons for sharing them on social media, deleting them, exporting them to EndNote, emailing them to yourself or a friend, or whatever). The user would probably want to email all the saved references to themselves in one go, rather than one at a time.
Although this is a design for a mobile device, it can also be used on the web.