You can easily achieve this in P6 Administrator by duplicating existing database instance configuration and making appropriate changes
Refer to below Doc Id on My Oracle Support(MoS)
How To Add Multiple Database Instances To P6 Web Access, P6 Integration API and P6 Web Services [ID 1139995.1]
You application server configuration should be powerful enough to support multiple database and not run out of resources.
P6Services make use of BREBootstrap file which has connection information for a single database instance. I am unsure if with the single instance of the service you can cater to multiple database.
However you should be able to run multiple instances of P6Services with different BREBootStrap files.