How do “badges” work?
yes, it is possible to award same badge multiple times like this on famous-question
You can see in this case the number of times the same badge has been awarded:
(image taken from Jon skeet)
Yes - there are several badges that you can be awarded numerous times.
Some gold badges that can be awarded more than once are -
Here is a link to a post containing all the relevant information for all the tags on the network -