  Scalarized black holes (BH) have been shown to form dynamically in
extended-scalar-tensor theories, either through spontaneous scalarization --
when the BH is unstable against linear perturbations -- or through a non-linear
scalarization. In the latter, linearly stable BHs can ignite scalarization when
sufficiently perturbed. These phenomena are, however, not incompatible and
mixed scalarization is also possible. We explore two aspects of the
Einstein-Maxwell-Scalar model: solutions containing, simultaneously, linear
(\textit{aka} standard) and non-linear scalarization; and the effects of having
one of the coupling constants with an 'opposite sign' to the one leading to
scalarization. Both points are addressed by constructing and examining the
mixed scalarization's domain of existence. An overall dominance of the
spontaneous scalarization over the non-linear scalarization is observed.
Thermodynamically, an entropical preference for mixed over the standard
scalarization (spontaneous or non-linear) exists. In the presence of counter
scalarization, a quench of the scalarization occurs, mimicking the effect of a
scalar particle's mass/positive self-interaction term.
