No. No other procession is possible in God but the procession of the Word (the Son) and of Love (the Holy Ghost) because the divine processions can be derived only from the actions which remain within the agent, i.e., in a nature which is intellectual: and in the divine nature these actions are two (the acts of intelligence and of will).
God understands and loves His own essence, truth and goodness.
God understands all things by one simple act; and by one act also He wills all things.
Hence there cannot exist in Him a procession of Word from Word, nor of Love from Love: for there is in Him only one perfect Word, and one perfect Love (thereby being manifested His perfect fecundity).