[A]s the Church Triumphant is but one in Heaven, so the Church Militant is but one in Earth; Therefore all the true Members thereof should study Unity, This Truth of the Oneness of the Catholick Visible Church, being the Ground of all the Union and Communion in the Ordinances thereof. . . . If the Church be One, Divisions and divided Communions in her must either infer that this one Church is many, made up of Heterogenous parts, or that the Church divided from is not a part of that one Church, and hath broken off from that which compacts the Body together.
Here, Shields recognizes the fact that when there are separated denominations, assuming a presbyterian system of church government, the necessary implication is that the separated churches are rejecting each others' de jure legitimacy and authority as churches (though not necessarily each others' de facto existence as churches). The only alternative to this is to deny the doctrine of the essential unity of the visible church for a congregationalist view of multiple independent "Bodies of Christ." Matthew Vogan, on p. 144 of the same article, quotes Shields as recognizing the un-presbyterian, congregationalist nature of the idea of multiple de jure denominations (the quotation is from p. 68 of Shield's book):
Shields is emphatic that an independent Church, gathered and constituted and “not Subordinate unto the National Church” with its own officers and “invested with all Church Power” is “Schism, if ever there was any in the World”. “For then, what shall become of Presbyterian Government and our Testimony for that against Independency, Sectarianism and Schism?”
For more, see here and in general here.