Equivalent Metric on Finite Set

Question

Suppose $(X, d)$ be a finite metric space. I agree that all the metrics on finite set X are equivalent.

Can any one prescribe the methodology to derive all equivalent metric to the metric $d$? Given a metric $d$ on a finite set $X$, how many precisely equivalent metric to $d$ possible?

Example: $\frac{d}{1+d}$ is also metric.

Answer 1

If $d$ is a metric, then $\lambda\cdot d$ is an equivalent metric to $d$ for any $\lambda\in\mathbf R$.

Assume that $X=\{x_1,\dots,x_n\}$. If $d$ is a metric on $X$, define $c_{i,j}:=d(x_i,x_j)$. The set of all possible metrics on $X$ is equipotent to a subset of $\mathbf R^{n^2}$, which is equipotent to $\mathbf R$.