You can configure a single MS to support multiple backend machines, so it's really a question of where you want processes to run. In a single metadata server environment, the trick is in how to route processes to the appropriate server. The spawner does not know which application is requesting a server process, so the only way to control which server is launched is by user-based authorizations. So, theoretically, you could grant ReadMetadata access to the DI server to DI Studio users (denying ReadMetadata to others), and granting ReadMetadata only to BI users for the BI server.
This works, if each user only ever needs to use the one application. But, as soon as you want the DI User to also use Enterprise Guide or Web Report Studio, then you will need to go beyond simply using authorization controls. For example, if you were okay with saying Web Report Studio users use one workspace server, and the desktop clients (like DI Studio and EG) would use the other workspace server, then you could configure a pooled workspace server for WRS, where only the puddle IDs have ReadMetadata access to the physical server definition in metadata.
There are other factors that come into play if you want to keep DI Studio and EG users separate. But, it's probably too long to discuss all the different configurations here. The main point of this response, is that control of servers is governed by user-based metadata permissions, and not by application usage.
If you really need the application segregation, then you could consider multiple metadata servers. The issue there will be administrative overhead (since you're now maintaining two metadata servers), and ensuring shared content stays in synch in both metadata servers.