".... expect any problem of sharing the same Moodle within different organisations."
Will give just one example without a lot of detail ...
Company A doesn't want to see blogs, wikis, chat modules in the pick list when they start to create an activity/resource. So you, as an admin, hide those mods.
Company B, however, does want 'chat'.
The hiding of those is system wide ... no alternatives to choose for Company A no and Company B yes. That's a stock Moodle.
There is a multitenacy fork of Moodle that supposedly allows ... and one could find the repo for it and install ... but support for that is usually not a topic in these community forums.
While it sounds like more admin it's not that much ... virtual apaches ... company A has companya.site domain, company B has companyb.domain ... they are separate instances ... own users, own modules, own addons, etc.
IF those are installed via git ... it's realatively easy to update / upgrade all sites or just the companies that want latest/greatest as opposed to company that is more 'conservative' and prefers to be near 'leading edge', but NOT on 'bleeding edge'.
My experience with such setups? 1 ISD, 2 high schools, 4 junior highs, 8 or so elementary schools. 1 beefy server. all sites on same box ... spartans.tld, warriors.tld - example of the 2 HS's. Each campus could do as they liked ... without having to worry about how what they were doing affected the JHS or Elementary campuses. Each campus used LDAP for authentication restricted to campus OU's.
Updates to Moodles ... for all 14 instances took about 1 hours time ... and that was with backups to code, DB, and minimal data backups.
Am certain others might add their two cents. ;)
'spirit of sharing', Ken