Many ObjectDB users use ObjectDB with multiple databases. It is very easy when accessing databases directly (by database path). It is more tricky when using ObjectDB within an application server as automatic injection of entity managers in Java EE and JPA is static.
ObjectDB supports a dynamic schema, if your application generates entity classes dynamically (e.g. using CGLIB, javassist, asm, bcel). However, you will lose one of the main benefits of using a Java object database, which is the simplicity of representing persisted data using staticially defined POJO classes. A popular alternative approach it to use static Java classes for the common data and maps (as persistent fields) to store specific tenant data as key/value pairs.