I looked at Oskari, a map solution for websites:
https://joinup.ec.europa.eu/node/143095 http://oskari.org
The source code appears to be available:
The server (backend and frontend) is dual-licensed under the EUPL and MIT licenses. The backend is written in Java, the frontend in Javascript. It uses various other Libre components (such as PostgreSQL/PostGIS).
It looks like it should be possible to set this up if you are familiar with putting Java web services into production - not something I have experience with, but I'm sure others could manage it. The documentation seems to cover this:
http://oskari.org/documentation
I haven't dug too deeply into this. It looks like a Free Software solution that shouldn't be too hard for someone to set up if they know what they're doing. It has apparently already been reused internationally, according to the description.
David