“The other two relations are not opposed to either of these, but are opposed to each other; therefore these two cannot belong to one person: hence either one of them must belong to both of the aforesaid persons; or one must belong to one person, and the other to the other. Now, procession cannot belong to the Father and the Son, or to either of them; for thus it would follows that the procession of the intellect, which in God is generation, wherefrom paternity and filiation are derived, would issue from the procession of love, whence spiration and procession are derived, if the person generating and the person generated proceeded from the person spirating; and this is against what was laid down above (27, 3 and 4). We must frequently admit that spiration belongs to the person of the Father, and to the person of the Son, forasmuch as it has no relative opposition either to paternity or to filiation; and consequently that procession belongs to the other person who is called the person of the Holy Ghost, who proceeds by way of love, as above explained. Therefore only three persons exist in God, the Father, the Son, and the Holy Ghost.”
I am not sure exactly what Aquinas l is saying here. It seems to me that he is saying that the known three persons may not be further divided, and do not produce of themselves further persons. This does not address the question I am asking which is whether further persons, unknown to us, might exist.