  We construct a multiplicity distribution characterized by large factorial
cumulants (integrated correlation functions) from a simple combination of two
ordinary multiplicity distributions characterized by small factorial cumulants.
We find that such a model, which could be interpreted as representing two event
classes, reproduces the preliminary data for the proton cumulants measured by
the STAR collaboration at $7.7$ GeV very well. This model then predicts very
large values for the fifth and sixth order factorial cumulants, which can be
tested in experiment.
