The whole undivided divine nature is in each divine person simultaneously and eternally. The modifying of divine nature by eternal generation and spiration does not divide the nature, as temporal generation does, but leaves it whole and entire, so that the substance of the begotten Son and the spirated Spirit is numerically and identically that of the unbegotten and unspirated Father. (p. 278).
Shedd then proceeds to discuss how the three persons relate each to the others. I quote him at length,
Revelation clearly teaches that these personal characteristics are so marked and peculiar that the three divine persons are objective to each other. God the Father and God the Son are so distinct from each other that some actions which can be ascribed to the one cannot be ascribed to the other. The Father "sends" the Son; this act of sending the Son cannot be attributed to the Son. The Father "loves" the Son; this act of loving the Son cannot be ascribed to the Son. An examination of the Scriptures gives the following series of twelve actions and relations of the three trinitarian persons, which prove that they are objective to one another, that one may do or experience something that is personal to himself and is not personal to the others. One divine person … loves another (John 3:35) dwells in another (John 14:10–11) suffers from another (Zech. 13:7) knows another (Matt. 11:27) addresses another (Heb. 1:8) is the way to another (John 14:6) speaks of another (Luke 3:22) glorifies another (John 17:5) confers with another (Gen. 1:26; 11:7) plans with another (Isa. 9:6) sends another (Gen. 16:7; John 14:26) rewards another (Phil. 2:5–11; Heb. 2:9) Here are twelve different actions and relations which demonstrate that the Father, Son, and Holy Spirit are not one and the same person. (p. 279).
Each person of the Trinity stands in an 'I"-"Thou" relation to the others. Shedd teases out what that means for the divine self-consciousness, "And the three persons are so real and distinct from each other that each possesses a hypostatic or trinitarian consciousness different from that of the others. The second person is conscious that he is the Son and not the Father, when he says, "O Father, glorify me" (John 17:5). The first person is conscious that he is the Father and not the Son, when he says, "You are my Son, this day have I begotten you" (Heb. 1:5). The third person is conscious that he is the Spirit and neither the Father nor the Son, when he says, "Separate me Barnabas and Saul for the work whereunto I have called them" (Acts 13:2)." (p. 282).
But that does not mean that the divine persons are three individual centres of self-consciousness, akin to three human persons having a chat. Shedd is no social Trinitarian. He explains, "These three hypostatic consciousnesses constitute the one self-consciousness of divine essence. By reason of and as the result of these three forms of consciousness, divine essence is self-contemplative, self-cognitive, and self-communing. Though there are three forms of consciousness, there are not three essences or three understandings or three wills in the Godhead because a consciousness is not an essence or an understanding or a will. There is only one essence, having one understanding and one will. But this unity of essence, understanding, and will has three different forms of consciousness: paternal, filial, and spiritual because it has three different forms of subsistence, namely, the Father, the Son, and the Spirit." Shedd draws an analogy between the divine essence in relation to the persons and the divine self-consciousness and the hypostatic/personal consciousnesses, "As the one divine essence is the same thing with the three persons, and not a fourth different thing by itself, so the one divine self-consciousness is the same thing with the three hypostatic consciousnesses and not a fourth different thing by itself." (p. 282-283).
Shedd's handling of the doctrine of the Trinity has relevance for debates within Evangelicalism on the Eternal Relational Submission (ERS) of the Son to the Father. Advocates of ERS sometimes argue that classic Trinitarianism fails to do justice to divine personhood, having little to say beyond the eternal relations of origin. As Shedd makes clear, however, Father, Son and Holy Spirit each stand in an "I"-"Thou" relation to the others. But that does not mean we should attribute an individual will to each person, or posit that each is a distinct centre of self-consciousness. As Shedd rightly underlines, will is an attribute of the divine being and there is only one self-consciousness in God. The theologian's distinction between the personal consciousness of the Father, Son and Holy Spirit and the singular divine self-consciousness is a useful safeguard against social Trinitarianism. "The three hypostatical [personal] consciousnesses in their combination and unity constitute the one self-consciousness." (p. 283).
You never know what useful stuff may be found lying around in the Shedd. I may rummage around a little more.
Quotations from Dogmatic Theology Volume I, Klock & Klock 1979 reprint. You can also find a e-copy online, but the pagination is different, here. See p. 5 of the PDF for clickable contents.