No. If the personal relations are mentally abstracted, the hypostases no longer remain because relation distinguishes and constitutes the hypostases.
As regards the abstraction of the form from the matter, if the non-personal properties are removed, then the idea of the hypostases and persons remains; as, for instance, if the fact of the Father's being unbegotten or spirating be mentally abstracted from the Father, the Father's hypostasis or person remains.
If, however, the personal property be mentally abstracted, the idea of the hypostasis no longer remains. For the personal properties are not to be understood as added to the divine hypostases, as a form is added to a pre-existing subject: but they carry with them their own "supposita," inasmuch as they are themselves subsisting persons; thus paternity is the Father Himself. For hypostasis signifies something distinct in God, since hypostasis means an individual substance.
Person does not add to hypostasis a distinguishing property absolutely, but a distinguishing property of dignity, all of which must be taken as the difference. Now, this distinguishing property is one of dignity precisely because it is understood as subsisting in a rational nature. Hence, if the distinguishing property be removed from the person, the hypostasis no longer remains; whereas it would remain were the rationality of the nature removed; for both person and hypostasis are individual substances. Consequently, in God the distinguishing relation belongs essentially to both.