Lighten white/gray background

Continuing the discussion from How to Remove a whitebackground but keep the shadows?:

I have a pictures from a photographer that was taken on a white background. Is there a way to make the white look whiter without losing the shadows on the kids in the picture? if i try to select the background to lighten it with levels, it selects also the shadows, and they end up getting lost.
Any suggestions?

what about trying with adjustment layers and then masking the parts that you need less or more?
or using the dodge tool? but do it very slow and with low flow!

thanks! it’s definitely better that what i was doing before, but its going to be a lot of work if i want it to look perfect. And its a lot of photos that im editing.