On what basis do Catholics continue doctrinal development after the Bible canon was closed? On what basis do Catholics continue doctrinal development after the Bible canon was closed?
The Catholic Church teaches dogmatically that general revelation ended with the Apostles (cf. condemned proposition no. 21 in Pope St. Pius X's Lamentabili Sane). This general revelation forms the Deposit of the Faith, which is taught and explained by the Church.
We see through history that Church fathers, saints, and theologians have explained the Deposit of the Faith in new ways. Per Catechism of the Catholic Church ¶ 66,

Yet even if Revelation is already complete, it has not been made completely explicit; it remains for Christian faith gradually to grasp its full significance over the course of the centuries.

Obviously, new explanations must be judged prudently by the Church, lest contradiction or novelty be introduced. St. John Henry Newman, in An Essay on the Development of Christian Doctrine, shows a set of principles by which genuine development may be judged. Summarily, these are:


Preservation of Type
Continuity of Principles
Power of Assimilation
Logical Sequence
Anticipation of Its Future
Conservative Action upon Its Past
Chronic Vigor