Blender has a feature called "shrinkwrapping" and judging from a google search for "shrinkwrapping 3dsmax" there are a few scripts that will give you the same functionality in 3dsmax.
Not a max user though, so this may not be the most efficient solution.
In the freeform tools on the ribbon, there's a section called PolyDraw. It has a tool in it called Conform that lets you paint over a mesh, conforming it to the surface beneath it.
in your spefic use case you got in the screen shot why would'nt you just duplicate the polygons from the object your trying to conform too and use those?
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Not a max user though, so this may not be the most efficient solution.
Thanks all!