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 vs. log[OIII]/H 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.