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Abstract. In 2008, Haglund, Morse and Zabrocki [16] formulated a Compositional form of the Shuffle Conjecture of Haglund et al. [15]. In very recent work, Gorsky and Negut by combining their discoveries [14], [19] and [20], with the work of Schiffmann-Vasserot [22] and [23] on the symmetric function side and the work of Hikita [17] on the combinatorial side, were led to formulate an infinite family of conjectures that extend the original Shuffle Conjecture of [15]. In fact, they formulated one conjecture for each pair (m,n) of coprime integers. This work of Gorsky-Negut leads naturally to the question as to where the Compo-sitional Shuffle Conjecture of Haglund-Morse-Zabrocki fits into these recent developments. Our discovery here is that there is a compositional extension of the Gorsky-Negut Shuffle Conjecture for each pair (km, kn), with (m,n) co-prime and k> 1