Fork
Basically, if the license of the original software allows, you can copy the code to develop your own version of it, with your own additions, which will be a "fork".
Forks are often seen in free and open source software development. This is now a more popular term thanks to contribution model using Git (and/or the GitHub platform).
See also
- Fork on Wikipedia
- How to fork a GitHub repo (fork as in a Git context)
- Fork (Glossary)
- Various "well-known" forks