Developing tissues are patterned by coordinated activities of signaling systems, which can be integrated by a regulatory region of a gene that binds multiple transcription factors or by a transcription factor that is modified by multiple enzymes. Based on a combination of genetic and imaging experiments in the early Drosophila embryo, we describe a signal integration mechanism that cannot be reduced to a single gene regulatory element or a single transcription factor. This mechanism relies on an enzymatic network formed by Mitogen Activated Protein Kinase (MAPK) and its substrates. Specifically, anteriorly localized MAPK substrates, such as Bicoid, antagonize MAPK-dependent downregulation of Capicua, a repressor which is involved in gene regulation along the dorsoventral axis of the embryo. MAPK substrate competition provides a basis for ternary interaction of the anterior, dorsoventral, and terminal patterning systems. A mathematical model of this interaction can explain gene expression patterns with both anteroposterior and dorsoventral polarities.