Yes. We speak of one essence of the three persons, and three persons of the one essence, provided that these genitives be understood as designating the form because in God the persons are multiplied, and the essence is not multiplied.
Form, in the absolute sense, is wont to be designated as belonging to that of which it is the form, as we say "the virtue of Peter." On the other hand, the thing having form is not wont to be designated as belonging to the form except when we wish to qualify or designate the form. In which case two genitives are required, one signifying the form, and the other signifying the determination of the form, as, for instance, when we say, "Peter is of great virtue [magnae virtutis]," or else one genitive must have the force of two, as, for instance, "he is a man of blood"--that is, he is a man who sheds much blood [multi sanguinis].
So, because the divine essence signifies a form as regards the person, it may properly be said that the essence is of the person; but we cannot say the converse, unless we add some term to designate the essence; as, for instance, the Father is a person of the "divine essence"; or, the three persons are "of one essence."
In the objects of the senses (whence the intellect derives its knowledge) the nature of the species is made individual by the matter, and thus the nature is as the form, and the individual is the "suppositum" of the form.
So also in God the essence is taken as the form of the three persons, according to our mode of signification. (Divine things are named by our intellect, not as they really are in themselves -- for in that way it knows them not -- but in a way that belongs to things created.)
Only those things can be said to be of "one essence" which have one being. So the divine unity is better described by saying that the three persons are "of one essence," than by saying they are "of one nature."
Because "nature" designates the principle of action while "essence" comes from being [essendo], things may be said to be of one nature which agree in some action, as all things which give heat.
Augustine says (Contra Maxim. iii) that the word homoousion, which the Council of Nicaea adopted against the Arians, means that the three persons are of one essence.
Hilary says (De Synod.): "It would be prejudicial to holy things, if we had to do away with them, just because some do not think them holy. So if some misunderstand homoousion, what is that to me, if I understand it rightly? . . . The oneness of nature does not result from division, or from union or from community of possession, but from one nature being proper to both Father and Son."