This is one I would have to look at to know what kind of paper your dealing with. This would be the best way to handle a paper that was strippable and was pre-pasted, not a fabric backed vinyl.
Take a piece of coarse sandpaper and carefully score the surface of the offending wallpaper well enough to open the face of it, then wet it with a sponge soaked with water only. Work in small enough areas to avoid soaking the paper that you want to save. This could take you a while. When your done, wash the walls thoroughly to make sure that you remove all the paste residue. Hopefully the process wont release the paste from the paper underneath
I have hung Wallcoverings for over 20 years and have much knowledge, feel free to email me with any other questions