Cardinality of the sets of dimension functions in ordered structures

We compute the cardinality ${\mathfrak{n}}_{\dim }(\mathcal{M})$ of the sets of dimension functions on the ordered structures $\mathcal{M}$. The inequality ${\mathfrak{n}}_{\dim }(\mathcal{M})\le 1$ holds if $\mathcal{M}$ is a d-minimal expansion of an ordered group. If $\mathcal{M}$ is o-minimal and ${\mathfrak{n}}_{\dim }(\mathcal{M})<\mathrm{\infty }$, there exists a positive integer $m$ such that ${\mathfrak{n}}_{\dim }(\mathcal{M})=2^m-1$. For every positive integer $m$, there exists a weakly o-minimal expansion $\mathcal{M}$ of an ordered divisible Abelian group such that ${\mathfrak{n}}_{\dim }(\mathcal{M})=m$.