Once in awhile I am asked about installing new wallpaper over old. I have experienced the results of this both as an installer and as a remover and can not recommend it, except in special circumstances.
Some people might perceive that installing new wallpaper over existing wallpaper will save time and money. However, the end results are never satisfactory, and the homeowner is faced with the choice of living with a hack job or removing both layers of wallpaper, buying a second batch of new wallpaper, and having it reinstalled. Nothing will have been saved.
The problem is that no matter how secure the existing coat of old wallpaper may seem to be, the moisture from the new paste will migrate to the original paste and loosen it. The results will be several square feet of unattached wallpaper that literally billows in the breeze. To be fair, most of the paper will remain secured, but who wants to live with just "most" of the paper looking good? Is it really worth saving a few dollars by not stripping the old paper? Wallpaper when properly installed will last for many years but will also be easily removed.
My most notable experience with stripping multiple layers was an old farm house in Sherborn that had five layers of wallpaper in the dining room. Two of those layers had been painted. Needless to say, the time and expense of removing all those layers far outweighed any savings if each layer had been removed prior to redecorating. If one feels that an immediate saving of time and money will be realized TODAY by painting or wallpapering over old wallpaper, please consider that SOMEDAY it will all need to be removed and the job will be many times more difficult and costly.
Here's one exception to this rule. There are rare occasions where either an unknowing homeowner or an unscrupulous contractor has hung paper directly on top of gypsum wallboard. Stripping that paper is basically impossible without destroying the face of the sheetrock. The good news is that the paper is now married to and has become one with the cardboard facing of the gypsum wallboard. The solution is to find all loose areas of paper and peel them off. Once all loose areas are removed, everything should be primed with a good penetrating drywall-repair-sealer. Patching and sanding where necessary can then be performed and a final prime coat will make the walls ready for the new wallpaper. When these procedures are followed, the new wallpaper will stay stuck to the walls and will be strippable when the time comes.
In truth, new wallpaper can be hung on old wallpaper. Yes, a little savings might be realized ..... temporarily. One day the full price will be paid, with interest. The possibility of immediate failure is high and the difficulty of future removal is assured.