Carefully ;) One option is to build your app to check for migrations on startup. I've run systems that'd do schema migrations on a per user basis for data stored in objects per user, and it worked just fine across a userbase of a couple of million accounts, on the basis that the only clients that connect directly also owns the schema, so nothing ever connects without immediately checking if a migration needs to run.

But consider that for setups like this the database might well be the customers own database, so their schema might not be something it's your job to touch at all.