How to copy rows into same table efficiently

Dear PG experts,

We have a tenant discriminator column in our tables to enable storage of
data from multiple
tenants. This column is also part of the composite primary key.
The customers may request creation of a tenant copy, which means if they
currently have a
tenant id "ABCD", they would like to copy all data "where tenant_id =
'ABCD'" to a new copy tenant "XYZ".
The copy must also be done on the same table.

Current approach taken is to build a query like below:
INSERT INTO mytable (col1, col2, col3, col4) SELECT col1, 'XYZ', col3, col4
FROM mytable WHERE col2 = 'ABCD'

Is there a better way to do this?
There could be other tables with foreign key reference, would a simple
ordering of the copy based on table relationship suffice?
Also if the table has millions of records, what are the things to take care
of?

Regards,
Arun Suresh