Six levels exist to the Magisterium, the teaching authority, of the Catholic Church. The first five of these levels require as a minimum the religious assent of the Catholic faithful. The six levels consist of (1) pronouncements of the Pope that are made ex cathedra (extraordinary magisterium), (2) the Bishops in communion with the Pope, defining doctrine at a General Council (extraordinary magisterium); (3) the Bishops in communion with the Pope and together with him, proposing definitely, dispersed, but in agreement (ordinary and universal magisterium); (4) the Pope himself (ordinary magisterium), (5) the Bishops in communion with the Pope (ordinary magisterium), and (6) theologians (magisterium cathedrae magistralis).
The Pope has what is known as his own ordinary magisterium (#4 above), his own teaching authority, and this by divine appointment (Mt 16:18–19). This is separate from, and in addition to, any pronouncements he might make ex cathedra (#1 above).
The Magisterium of the Catholic Church is neither external to the Pope nor separate from him (#1 through #6 above). In fact, for the teaching authority, the magisterium, of the bishops throughout the world to be valid and authentic, it necessarily has to be in communion with the Pope.
The Magisterium is neither external to the Pope nor optional with regard to its acceptance and the subjection to it by all the Catholic faithful, because it is the Pope who (1) by divine appointment, has supreme and full authority over the universal Church, including, but not limited, to the Catholic Church itself; and (2) is the Supreme Guarantor, the Supreme Witness, of the Faith by virtue of the charism of truth and the charism of a faith that never fails granted to him, and to him alone, by God as an intrinsic part of the privileges of his office as the Vicar of Christ.