Some of these authorities are the New Testament itself, the Fathers of the Church, the Church in Council (cf. Acts 15 model), the "faithful people" faithful to what was handed down to them, etc. The Spirit of Truth is entrusted to faithful people as an authority in the Church. The fuller sense of any  Scripture text has to be in agreement with the literal sense of the words. This fuller sense must be a consequential development of what the human author of the text intended to say.
An example of the fuller sense in the interpretation of Scripture is found by looking at the New Testament. In the Gospel according to Matthew, Chapter 1, verse 23, Matthew says that the conception of Jesus by Mary was a virginal  conception and took place so that the words of the prophet Isaiah (7:14) might be fulfilled. Isaiah gives no evidence that the prophet had Jesus' conception in the womb of Mary in mind.