Objection 1. It would seem that Extreme Unction is not one sacrament. Because the oneness of a thing depends on its matter and form, since being and oneness are derived from the same source. Now the form of this sacrament is said several times during the one administration, and the matter is applied to the person anointed in respect of various parts of his body. Therefore it is not one sacrament.
Objection 2. Further, the unction itself is a sacrament, for it would be absurd to say that the oil is a sacrament. But there are several unctions. Therefore there are several sacraments.
Objection 3. Further, one sacrament should be performed by one minister. But the case might occur that Extreme Unction could not be conferred by one minister: thus if the priest die after the first unction, another priest would have to proceed with the others. Therefore Extreme Unction is not one sacrament.
On the contrary, As immersion is in relation to Baptism, so is unction to this sacrament. But several immersions are but one sacrament of Baptism. Therefore the several unctions in Extreme Unction are also one sacrament.
Further, if it were not one sacrament, then after the first unction, it would not be essential for the perfection of the sacrament that the second unction should be performed, since each sacrament has perfect being of itself. But that is not true. Therefore it is one sacrament.
I answer that, Strictly speaking, a thing is one numerically in three ways. First, as something indivisible, which is neither actually nor potentially several--as a point, and unity. Secondly, as something continuous, which is actually one, but potentially several--as a line. Thirdly, as something complete, that is composed of several parts--as a house, which is, in a way, several things, even actually, although those several things go together towards making one. In this way each sacrament is said to be one thing, in as much as the many things which are contained in one sacrament, are united together for the purpose of signifying or causing one thing, because a sacrament is a sign of the effect it produces. Hence when one action suffices for a perfect signification, the unity of the sacrament consists in that action only, as may be seen in Confirmation. When, however, the signification of the sacrament can be both in one and in several actions, then the sacrament can be complete both in one and in several actions, even as Baptism in one immersion and in three, since washing which is signified in Baptism, can be completed by one immersion and by several. But when the perfect signification cannot be expressed except by means of several actions, then these several actions are essential for the perfection of the sacrament, as is exemplified in the Eucharist, for the refreshment of the body which signifies that of the soul, can only be attained by means of meat and drink. It is the same in this sacrament, because the healing of the internal wounds cannot be perfectly signified save by the application of the remedy to the various sources of the wounds. Hence several actions are essential to the perfection of this sacrament.
Reply to Objection 1. The unity of a complete whole is not destroyed by reason of a diversity of matter or form in the parts of that whole. Thus it is evident that there is neither the same matter nor the same form in the flesh and in the bones of which one man is composed. In like manner too, in the sacrament of the Eucharist, and in this sacrament, the diversity of matter and form does not destroy the unity of the sacrament.
Reply to Objection 2. Although those actions are several simply, yet they are united together in one complete action, viz. the anointing of all the external senses, whence arises the infernal malady.
Reply to Objection 3. Although, in the Eucharist, if the priest die after the consecration of the bread, another priest can go on with the consecration of the wine, beginning where the other left off, or can begin over again with fresh matter, in Extreme Unction he cannot begin over again, but should always go on, because to anoint the same part a second time would produce as much effect as if one were to consecrate a host a second time, which ought by no means to be done. Nor does the plurality of ministers destroy the unity of this sacrament, because they only act as instruments, and the unity of a smith's work is not destroyed by his using several hammers.
Source: Summa Theologica (New Advent)