A clear visualization of a two-way ANOVA To provide a full yet simple picture of a 3-level, one-way ANOVA, I use the following visualization where variation within each group (the filled circles) and variation between the groups (black arrows) are simple to be understood.

But I'm wondering if it could be possible to extend the current visualization to a 2 x 3 two-way ANOVA (adding another way with two groups to the current visualization)?

(Note: the dashed vertical lines denote each group's mean)
You could go for a 3D plot, but they are only useful in specific situations (e.g. simple bar plot, a surface etc.), and definitely not here. Your best option, while keeping the overall design of your plot, seems to be to split your data by the factor with 2 levels, and plot each separately in 2 panels side by side. That way, you can compare similarities, baseline shifts, and interactions.