  The description of unitary few-boson systems is conceptually simple: only one
parameter -- the three-body binding energy -- is required to predict the
binding energies of clusters with an arbitrary number of bosons. Whether this
correlation between the three- and many-boson systems still holds for two
species of bosons for which only the inter-species interaction is resonant
depends on how many particles of each species are in the system. For few-body
clusters with species $A$ and $B$ and a resonant $AB$ interaction, it is known
that the emergent $AAB$ and $ABB$ three-body scales are correlated to the
ground-state binding energies of the $AAAB$ and $ABBB$ systems, respectively.
We find that this link between three and four bodies is broken for the $AABB$
tetramer whose binding energy is neither constrained by the $AAB$ nor by the
$ABB$ trimer. From this de-correlation, we predict the existence of a scale
unique to the $AABB$ tetramer. In our explanation of this phenomenon, we
understand the $AABB$ and $AAAB$/$ABBB$ tetramers as representatives of two
different universal classes of $N$-body systems with distinct
renormalization-group and discrete-scaling properties.
