The notochord is a defining feature of the chordates. The transcription factor Brachyury (Bra) is a key regulator of notochord fate but here we show that it is not a unitary master regulator in the model chordate Ciona. Ectopic Bra expression only partially reprograms other cell types to a notochord-like transcriptional profile and a subset of notochord-enriched genes is unaffected by CRISPR Bra disruption. We identify Foxa.a and Mnx as potential co-regulators, and find that combinatorial cocktails are more effective at reprogramming other cell types than Bra alone. We reassess the network relationships between Bra, Foxa.a and other components of the notochord gene regulatory network, and find that Foxa.a expression in the notochord is regulated by vegetal FGF signaling. It is a direct activator of Bra expression and has a binding motif that is significantly enriched in the regulatory regions of notochord-enriched genes. These and other results indicate that Bra and Foxa.a act together in a regulatory network dominated by positive feed-forward interactions, with neither being a classically defined master regulator.