You can build 21 data marts in SSAS and still link them through linked measure groups and linked dimensions (for example: Linked Measure Groups). However, I usually advice against these kind of set-ups, as it really complicates everything.

I'd rather built one (or a few more) SSAS cubes. You can logically seperate the model in the data source view using multiple diagrams and you can present parts of the cubes to users with perspectives. A downside is that it will take significantly longer to process the cube, as it contains everything. An upside is that you can reuse dimensions across different facts (called conformed dimensions).