Is it possible - and is so what is the right way - to create a Joomla 3 plugin that ads new functionality to an existing module or component. I have made some minor but useful UI functionality changes to a popular component and module that I would share with others. I feel that editing the source is not the way, a plugin would be best. Thanks!
Yes, Its possible Joomla plugin is designed for that purpose,
You can add more features to existing component or module using Joomla plugin events.
There are many extensions that are using this concept like extending default users component com_users, com_virtuemart etc.
If you are using UI features I think System plugin will help you to solve the challenges
For an example I made a new feature to com_virtuemart with Product Zoom facility , It uses System Plugin events .
Hope it make sense..