Objection 1. It would seem that no other procession exists in God besides the generation of the Word. Because, for whatever reason we admit another procession, we should be led to admit yet another, and so on to infinitude; which cannot be. Therefore we must stop at the first, and hold that there exists only one procession in God.
Objection 2. Further, every nature possesses but one mode of self-communication; because operations derive unity and diversity from their terms. But procession in God is only by way of communication of the divine nature. Therefore, as there is only one divine nature (11, 4), it follows that only one procession exists in God.
Objection 3. Further, if any other procession but the intelligible procession of the Word existed in God, it could only be the procession of love, which is by the operation of the will. But such a procession is identified with the intelligible procession of the intellect, inasmuch as the will in God is the same as His intellect (19, 1). Therefore in God there is no other procession but the procession of the Word.
On the contrary, The Holy Ghost proceeds from the Father (John 15:26); and He is distinct from the Son, according to the words, "I will ask My Father, and He will give you another Paraclete" (John 14:16). Therefore in God another procession exists besides the procession of the Word.
I answer that, There are two processions in God; the procession of the Word, and another. In evidence whereof we must observe that procession exists in God, only according to an action which does not tend to anything external, but remains in the agent itself. Such an action in an intellectual nature is that of the intellect, and of the will. The procession of the Word is by way of an intelligible operation. The operation of the will within ourselves involves also another procession, that of love, whereby the object loved is in the lover; as, by the conception of the word, the object spoken of or understood is in the intelligent agent. Hence, besides the procession of the Word in God, there exists in Him another procession called the procession of love.
Reply to Objection 1. There is no need to go on to infinitude in the divine processions; for the procession which is accomplished within the agent in an intellectual nature terminates in the procession of the will.
Reply to Objection 2. All that exists in God, is God (3, 3, 4); whereas the same does not apply to others. Therefore the divine nature is communicated by every procession which is not outward, and this does not apply to other natures.
Reply to Objection 3. Though will and intellect are not diverse in God, nevertheless the nature of will and intellect requires the processions belonging to each of them to exist in a certain order. For the procession of love occurs in due order as regards the procession of the Word; since nothing can be loved by the will unless it is conceived in the intellect. So as there exists a certain order of the Word to the principle whence He proceeds, although in God the substance of the intellect and its concept are the same; so, although in God the will and the intellect are the same, still, inasmuch as love requires by its very nature that it proceed only from the concept of the intellect, there is a distinction of order between the procession of love and the procession of the Word in God.
Source: Summa Theologica (New Advent)