  We obtain a sparse domination principle for an arbitrary family of functions
$f(x,Q)$, where $x\in {\mathbb R}^n$ and $Q$ is a cube in ${\mathbb R}^n$. When
applied to operators, this result recovers our recent works. On the other hand,
our sparse domination principle can be also applied to non-operator objects. In
particular, we show applications to generalized Poincar\'e-Sobolev
inequalities, tent spaces, and general dyadic sums. Moreover, the flexibility
of our result allows us to treat operators that are not localizable in the
sense of our previous works, as we will demonstrate in an application to
vector-valued square functions.
