  Quantum mechanical systems whose symmetry is given by $\mathbb{Z}_2^3$-graded
version of superconformal algebra are introduced. This is done by finding a
realization of a $\mathbb{Z}_2^3$-graded Lie superalgebra in terms of a
standard Lie superalgebra and the Clifford algebra. The realization allows us
to map many models of superconformal quantum mechanics (SCQM) to their
$\mathbb{Z}_2^3$-graded extensions. It is observed that for the simplest SCQM
with $osp(1|2)$ symmetry there exist two inequivalent $\mathbb{Z}_2^3$-graded
extensions. Applying the standard prescription of conformal quantum mechanics,
spectrum of the SCQMs with the $\mathbb{Z}_2^3$-graded $osp(1|2)$ symmetry is
analyzed.
  It is shown that many models of SCQM can be extended to
$\mathbb{Z}_2^n$-graded setting.
