This userscript displays a user's public organizations beyond the 25 GitHub now limits a user page to, as described in isaacs/github#840.
This app technically supports the rudimentary authorization flow for GitHub Enhancement Suite scripts. However, due to the lousy way GitHub implements organization read access for OAuth applications, this will most likely be unsatisfactory, if you're in a position (like me) where you need to be able to read an ever-increasing list of private organizations.
You can come up with your own way to fix this: the way I do it is to go into the "Storage" tab of Tampermonkey and add a "stuartpb access token" line with a manually-generated personal access token with read:org scope, since personal access tokens do give full read access for private organization access. (Obviously, you'd want to replace stuartpb with your own username.)
Copyright Stuart P. Bentley.
This work may be used freely as long as this notice is included.
The work is provided "as is" without warranty, express or implied.