While there isn't a way using bolt communication to stop and start a Neo4j dbms, if you're using 4.0.x with multi-databases, you can issue an administrative query to the system database to stop and start the databases that are present:
No, community edition only has the single neo4j database for data. The system db is reserved for user/database/role/security administration and can't be used as any kind of general purpose db.
So you can't do this with a single dbms.
You would need to spin up potentially several Neo4j instances, and then in your client have it manage the driver connections to each one.
You might want to take a look at Neo4j Aura for the future, though. This is our db-as-a-service offering...not free, but affordable, and backed by a 3-instance enterprise-edition cluster.
It hasn't been readied for 4.0 yet, that's in-progress, but when it does you might consider it for handling your multi-db needs.