In the past I worked at a company that managed thousands of individual MSSQL databases for individual customers due to data security concerns. Effectively what happened is the schema became locked in place since running migrations across so many databases became hard to manage.

I currently work at a company where customers have similar concerns around data privacy, but we've been to continue using a single multitenant DB instance by using PostgreSQL's row level security capabilities where rows in a table are only accessible by a given client's database user:

https://www.postgresql.org/docs/9.5/ddl-rowsecurity.html

We customized both ActiveRecord and Hibernate to accommodate this requirement.