  We use three seminal approaches in the study of fixed point theory, the so
called $G$-metrics, multidimensional fixed points and partially ordered spaces.
  More precisely, we extend known results from the theory of quasi-pseudometric
spaces to the $G$-metric space setting. In particular, we show the existence of
$n$-tuple fixed points (resp. common $n$-tuple fixed point) for a
non-decreasing mapping (resp. a pair of weakly related mappings) in a
$\phi$-ordered $G$-metric space.
