I think in order to make this work you'll need to create a new set of individual entry archive templates. Go into Templates and create a new archive template. Call it something like Individual Entry Pop-Up or whatever you want. Design this template however you want it to look and put the <$MTEntryMore$> tag in where you want the extra text to appear.
Next, go into Blog Config | Archiving and select to add new. For archive type select Individual and for Template select the new Individual Entry Pop-Up template that you created.
You'll want to give it a unique name in the Archive File Template field such as
<$MTEntryID pad="1"$>_more.html or something similar.
After you've done all this, rebuild your blog to create the new archive pages.
The final step is to add the javascript code that calls the pop-up. You can modify this from the javascript code that calls the comments pop-up.
In the <head> section of your index template, you'll have something like:
CODE
<script language="javascript" type="text/javascript">
function OpenMore (c) {window.open(c,'more','width=250,height=250,scrollbars=yes,status=yes');}
</script>
Then somewhere between your <MTEntries> tags add the following:
CODE
<MTEntryIfExtended>
<a href="http://path.to/<$MTEntryID pad="1"$>_more.html" onClick="OpenMore(this.href);return false">View more info</a>
</MTEntryIfExtended>
Now when you go to post a new entry to your blog, put the extra info in the Extended Entry field. If you do put info there, a link to the pop-up will be displayed on your blog and the pop-up will display the extra info.