There are two ways to make multiple links to the same destination URL in Bitly:
Use UTM parameters to create multiple links to the same URL
If you add UTM parameters to your long URL before shortening your links, you can create distinct versions of the link that all point to the same destination. For example, to create three separate links to support.bitly.com, UTM parameters could be used like this:
Each of these links points to support.bitly.com but can be shortened separately, giving us three separate Short Links:
Anyone can use a tool like Google's Campaign Builder to add UTM parameters to your links or add them manually before you shorten your links.
Edit the back-half of a link to create multiple versions
When you edit a link, previous versions of the link still work. This gives you multiple Short Links that each point to the same destination URL.
Two things to note about this method: It isn't possible to track the links' analytics separately, and the Links page only shows the most recent version of the link. All of them still work, however. Learn more at What happens when I change a link's back-half? and How do I find previous versions of a link?