In a previous paper we have defined a graph transformation that applies rewrite rules simultaneously to an input graph (or object in a suitable category), called the \emph{Global Coherent Transformation}. The expressiveness of this transformation is enhanced by enabling the use of \emph{subsumption morphisms} between rules and between direct (individual) transformations. Since this transformation is not committed to a particular approach to graph rewriting, it is formalized in a general representation of such approaches, called a \emph{Rewriting Environment}. It was shown that environments exist for the Double Pushout (DPO), the Sesqui-Pushout and the Pullback-Pushout approaches, that each satisfy a certain \emph{Correctness Condition}. In the present paper an environment is exhibited for the Single-Pushout (SPO) approach in categories of presheaves, and it is shown that the Correctness Condition holds. The link between SPO and DPO direct transformations is extended to subsumptions and expressed in diagrammatic form.