i dont do stairway cleaning/close cleaning (we do external power washing to HGV/brickwork & internal builders cleans)
i know someone who does the close cleaning, if you can phone any local factors in your area and ask to be put on the pricing list/tender list, thats what worked for him, he also approached local councils and housing associations for similar.
councils need to public the larger contracts online to tender and bid but the smaller ones from factors tend to be all in house pricing