Broken idiom alert. This sign at the National Skin Centre pharmacy says:
Mind Your Steps!
I think in the US we’d be more likely to say “watch your step” rather than “mind your step”, but pluralizing ‘step’ would be wrong in either case.
Sure, it’s logical that you’d want to be careful over the course of many steps, but conventionally, that’s not what we say.
I think we use the singular noun because this ‘step’ really means ‘manner of walking’. Here are some examples that showcase this singular sense of ‘step’.
The job promotion put a spring in his step.
The dancer has a graceful and lovely step.
The thief listened for the confident step of the policeman.
There is room for confusion because ‘step’ more often means ‘footstep’, and footsteps are often potentially plural, even when they are not syntactically plural.
The craftsman hoped his son would follow in his (foot)steps.
The sound of (foot)steps faded away down the hall.
Every (foot)step brought her closer to her goal.
Now that I think about it, the noun ‘stride’ has a similar duality: the singular noun means a manner of walking and the plural noun is used to refer to a series of individual movements.
I think there’s also pressure to pluralize ‘step’ coming from the common use of ‘steps’ to mean ‘stairs’.
The spilled water cascaded down the steps.
Anyway, the upshot is that the warning to “watch your step” or “mind your step” means “pay attention to your manner of walking”, not “pay attention to each of your footsteps”.