Objection 1. It would seem that a man cannot be absolved from one excommunication without being absolved from all. For an effect should be proportionate to its cause. Now the cause of excommunication is a sin. Since then a man cannot be absolved from one sin without being absolved from all, neither can this happen as regards excommunication.
Objection 2. Further, absolution from excommunication is pronounced in the Church. But a man who is under the ban of one excommunication is outside the Church. Therefore so long as one remains, a man cannot be loosed from another.
On the contrary, Excommunication is a punishment. Now a man can be loosed from one punishment, while another remains. Therefore a man can be loosed from one excommunication and yet remain under another.
I answer that, Excommunications are not connected together in any way, and so it is possible for a man to be absolved from one, and yet remain under another.
It must be observed however that sometimes a man lies under several excommunications pronounced by one judge; and then, when he is absolved from one, he is understood to be absolved from all, unless the contrary be expressed, or unless he ask to be absolved from excommunication on one count only, whereas he was excommunicated under several. On the other hand sometimes a man lies under several sentences of excommunication pronounced by several judges; and then, when absolved from one excommunication, he is not therefore absolved from the others, unless at his prayer they all confirm his absolution, or unless they all depute one to absolve him.
Reply to Objection 1. All sins are connected together in aversion from God, which is incompatible with the forgiveness of sin: wherefore one sin cannot be forgiven without another. But excommunications have no such connection. Nor again is absolution from excommunication hindered by contrariety of the will, as stated above (Article 2). Hence the argument does not prove.
Reply to Objection 2. Just as such a man was for several reasons outside the Church so is it possible for his separation to be removed on one count and to remain on another.
Source: Summa Theologica (New Advent)