Argentina's ministry of education did something like this with university software. The one used by students to sign up and by teachers to track grades, etc. There's a single open source modularised, customisable system made country-wide, and public universities customise it to their needs.
Before this initiative, every university was implementing their own software from scratch. In many cases, different faculties (e.g.: Engineering, Natural Sciences, Humanities, etc) each had their own software development teams developing their own independent software stack.