Combine multiple bar charts into one

I have 3 gantt charts that I would like to merge into 1 chart if it is possible. It is a gantt roadmap for future projects.

There are 3 sheets, one for each department "Shared services", "Supply" and "Range" (would like to keep it like this to make it easier for the users)
Each sheet has a gantt chart in the sheet "Roadmap gantt"

Is there some way to have a combined roadmap chart for all 3 departments without forcing the users to enter their projects into the same sheet?

Have attached an example file. Thanks!

It is a neat idea Kaper, thank you for replying. It's a great idea if the document was frozen and not edited anymore. I think that it would be tricky to update if there came a new project though? Or if there was an un-even amount of projects between the departments, which there are in reality. There would be extra rows that mess up the chart (at least when I tried it now).