  For the first time, we investigate susceptibilities of dense quark matter up
to $8$th order using an effective model. Generally higher order
susceptibilities will have more sign changes and larger magnitude, thus should
give more information about the presence and location of the conjectured QCD
critical end point (CEP). Two cases are studied, one with the CEP and one being
crossover phase transition throughout the QCD phase diagram. It is found that a
rapid crossover transition can also give similar sign pattern as the case with
the CEP and yield large signal. We propose that using several kinds of ions for
collision to search for a wider range on the QCD phase diagram may help.
