  In the recent paper, Bruce and Duplij introduced a double-graded version of
supersymmetric quantum mechanics (SQM). It is an extension of Lie
superalgebraic nature of ${\cal N}=1$ SQM to a $\mathbb{Z}_2^2$-graded
superalgebra. In this work, we propose an extension of Bruce-Duplij model to
higher values of $\cal N.$ Furthermore, it is shown that our construction of
double-graded SQM is a special case of the method which converts a given Lie
superalgebra to a $\mathbb{Z}_2^2$-graded superalgebra. By employing this
method one may convert a model of superconformal mechanics to its double-graded
version. The simplest example of ${\cal N}=1$ double-graded superconformal
mechanics is studied in some detail.
