Configure database mirroring for multiple databases via TSQL or Powershell when mirror is already restoring
Run the Alter Database command to add database to mirroring session 

--Run on Mirror
ALTER DATABASE Test_DB 
    SET PARTNER = 'TCP://Mirror_Me:5022'


Run on both mirror and principal. Remember to change the port numbers appropriately                                                                                    

--Run on Principal                                                                                     
ALTER DATABASE Test_DB
    SET PARTNER = 'TCP://Mirror_Me:5023'


Read this for more info.

Adding Additional script for a complete configuration minus the backup and restore process:

--This script allows db mirroring to be setup iwth a witness. 
--Edited to skip the backup and restore process to the mirror
--Make right configuraton changes accordingly

--On A server
    CREATE ENDPOINT [Endpoint_Mirroring] --change endpoint name as required
    STATE=STARTED
    AS TCP (LISTENER_PORT = 5022)  --change port number as required. default is 5022
    FOR DATA_MIRRORING
    (ROLE = ALL);

    GRANT CONNECT ON ENDPOINT::Endpoint_Mirroring TO [domain\login_name] --change to required domain account

--On B server
    CREATE ENDPOINT [Endpoint_Mirroring] --change endpoint name as required (good to keep the same name)
    STATE=STARTED
    AS TCP (LISTENER_PORT = 5022) --change port number as required. 
    FOR DATA_MIRRORING
    (ROLE = ALL);

    GRANT CONNECT ON ENDPOINT::Endpoint_Mirroring TO [domain\login_name] --change to required domain account


--Change for current db
    ALTER DATABASE TEST_DB SET PARTNER = 'TCP://servername.domainname.net:5022'  --change the database/server name
    GO

--On B server
    ALTER DATABASE TEST_DB SET PARTNER = 'TCP://servername.domainname.net:5022' --change the database/server name
    GO

--To setup Witness on Server C
    CREATE ENDPOINT [Endpoint_Mirroring] --change endpoint name as required (good to keep the same name)
    STATE=STARTED
    AS TCP (LISTENER_PORT = 5022) --change port number as required. 
    FOR DATA_MIRRORING
    (ROLE = ALL);

    GRANT CONNECT ON ENDPOINT::Endpoint_Mirroring TO [domain\login_name]


--On Principal Server
    ALTER DATABASE Test_DB SET WITNESS = 'TCP://servername.domainname.net:5022' --change the database/server name
    GO


NOTE: This does not contain setting up certificates for encrypted connections on the endpoints/mirroring. It does not hand transfer of logins from principal to mirror. This is outside the scope of this question.

DISCLAIMER: This script is AS-IS and should be thoroughly tested before implementing into a production environment.