A family of Microsoft word processing software products for creating web, email, and print documents.
There isn't a mechanism that will add symbols to the dialog. However, there are many symbol dialogs that you can access and then build your own favorites into auto text, scrapbook, or autocorrect.
From Insert > Symbol you can access not only the basic Symbol Browser dialog but also the Advanced Symbol dialog. Then there are the symbols that are part of your Operating System, which you access via System Preferences > Keyboard > Show Keyboard Character Viewer.
If you explore the Character Viewer options a bit you will find a plethora of characters that you can access.
Hope this helps