If you haven't done it yet, then print some slippery floor notices, ideally on yellow paper, and take some sticky backed plastic :
and stick a notice on every door and the top and bottom of every stairway and other doorways. I presume that the stairs have nosings so these could become extra slippery for everybody.
When cleaning the steps, have a towel with you and towel dry every stair and nosing as you go.
It might sound silly, but also check your liability insurance. There are often height restrictions, primarily intended for other trades. These can be used as a get out clause should there be an accident. If you phone your insurers, they will normally remove the restriction for CCers, but wont after a claim has been made.
Safe and happy cleaning
Ken