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A characteristic feature of the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> plaquette Ising and the X-Cube model is similar to that between the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> quantum transverse spin Ising model and the Toric Code. Gauging the <i>global</i> symmetry in the case of the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the <i>subsystem</i> symmetry of the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.