Can any binary operator be turned, through an associative operator, into another associative operator?

Question

Motivation: let $\circ:X^2\to X$ be some binary operator, and let $+:X^2\to X$ be some commutative operator. Then $$\star:X^2\to X:(x,y)\mapsto (x\circ y)+(y\circ x)$$ is commutative.

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I was wondering if there is some similar 'trick' for constructing associative operators from an arbitrary operator $\circ$.