  We introduce a new generalisation of partitions, multi-grounded partitions,
related to ground state paths indexed by dominant weights of Lie algebras. We
use these to express characters of irreducible highest weight modules of
Kac-Moody algebras of affine type as generating functions for multi-grounded
partitions. This generalises the approach of our previous paper, where only
irreducible highest weight modules with constant ground state paths were
considered, to all ground state paths. As an application, we compute the
characters of the level $1$ modules of the affine Lie algebras
$A_{2n}^{(2)}(n\geq 2)$, $D_{n+1}^{(2)}(n\geq 2)$, $A_{2n-1}^{(1)}(n\geq 3)$,
$B_{n}^{(1)}(n\geq 3)$, and $D_{n}^{(1)}(n\geq 4)$.
