Access to the source code allows small modifications without re-implementing the whole application from scratch.
Open source promotes reuse. Creating a spin-off in open source is called “Fork.”
Vim / Neovim
XEmacs was a fork of Emacs but (I believe) contributed many ideas back into Emacs itself
Emacs (What makes Emacs extensible?)
Everybody can create a Linux distro and there are tons of them
ErgoDox and its variants
ffmpeg as an extensible media pipeline