  A quantum mechanical model that realizes the $ \mathbb{Z}_2 \times
\mathbb{Z}_2$-graded generalization of the one-dimensional supertranslation
algebra is proposed. This model shares some features with the well-known Witten
model and is related to parasupersymmetric quantum mechanics, though the model
is not directly equivalent to either of these. The purpose of this paper is to
show that novel "higher gradings" are possible in the context of
non-relativistic quantum mechanics.
