  The binary bracket of a Courant algebroid structure on $(E,\langle
\cdot,\cdot \rangle)$ can be extended to a $n$-ary bracket on $\Gamma(E)$,
yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson
algebra and were defined, in an algebraic setting, by Keller and Waldmann. We
construct a higher geometric version of Keller-Waldmann Poisson algebra and
define higher multi-Courant algebroids. As Courant algebroid structures can be
seen as degree $3$ functions on a graded symplectic manifold of degree $2$,
higher multi-Courant structures can be seen as functions of degree $n\geq 3$ on
that graded symplectic manifold.
