  Two-dimensional (2D) line ratio diagnostic diagrams have become a key tool in
understanding the excitation mechanisms of galaxies. The curves used to
separate the different regions - HII-like or else excited by an active galactic
nucleus (AGN) - have been refined over time but the core technique has not
evolved significantly. However, the classification of galaxies based on their
emission line ratios really is a multi-dimensional problem. Here we exploit
recent software developments to explore the potential of three-dimensional (3D)
line ratio diagnostic diagrams. We introduce a specific set of 3D diagrams, the
ZQE diagrams, which separate the oxygen abundance and the ionisation parameter
of HII region-like spectra, and which also enable us to probe the excitation
mechanism of the gas. By examining these new 3D spaces interactively, we define
a new set of 2D diagnostics, the ZE diagnostics, which can provide the
metallicity of objects excited by hot young stars, and which cleanly separate
HII region-like objects from the different classes of AGNs. We show that these
ZE diagnostics are consistent with the key log[NII]/H$\alpha$ vs.
log[OIII]/H$\beta$ diagnostic currently used by the community. They also have
the advantage of attaching a probability that a given object belongs to one
class or to the other. Finally, we discuss briefly why ZQE diagrams can provide
a new way to differentiate and study the different classes of AGNs in
anticipation of a dedicated follow-up study.
