If you're looking to sell, don't wallpaper. Paint. Put up some inexpensive photos or "art". Wallpaper is too taste specific when selling.

Additionally, I'm not sure it will work to put paper over the paper, because of the vinyl surface.

I’ve not tried it, but I think your money would be better spent elsewhere.

If budget allows, I would first make sure the appliances are newer and all work (to include the water heater, ac and furnace), all the plumbing is in good working order, the house is sparkling clean (including power washing the exterior), any carpeting deep cleaned, roof and gutters are in good shape, landscaping spruced up, and paint (to include the front door if needed), I would save the papered walls for last; depending on what budget is left, I’d either clean them carefully and repair the spots that are coming up, or remove the paper properly, repair the drywall and paint.

Edit to add; all the outlets and switches work, too!

Tha would be a triple no. Don't apply new wallpaper over old, it always looks awful, telegraphing accumulting imperfections, don't bother with the "peel and stick for a while, except along the edges" wallpaper, and don't apply a finish that some fraction of potential buyers are going to dislike. Just strip the wallpaper and paint, everyone will be much happier.

"There's a lot to do so I have to be wise about where to invest the work" Then focus on CLEANING and being sure everything is in working order. If you have to strip the paper due to peeling that's unfortunate as that is a lot of work and time. You might try the fix it tubes of paste you can inject behind paper to restick it. But do not paint it or stick anything else on top. All that does is make a bad situation a nightmare for the next owner. Do not spend any more money than necessary. That means 'updating' isn't your focus. What should be is making things neat/tidy/clean/WORKING. Older homes people expect there to be design issues they are happy to make THEIR own. DO NOT buy appliances or repaint for color alone. What you choose will not be what they want!!! Even painting; NO ONE WANTS every surface painted quickly with white paint. Starter homes are tough to find. It will sell if clean in working order and priced well. You will not get a return on your investment if you start replacing things that work!!!

Here, in this article are various ways to cover existing wallpaper - including covering it with new wallpaper. A number of other options mentioned as well, including painting over the existing paper. https://dressyourhome.in/11117/how-to-cover-up-that-old-wallpaper-without-taking-it-down

And this link has specific info re using peel and stick wallpaper over existing wallpaper: https://www.limitlesswalls.com/blogs/blog/can-you-put-removable-wallpaper-over-existing-wallpaper

If you are using wallpaper - I recommend just using a solid color with texture - such as a grass cloth type look, etc. You are selling the house; and a patterned wallpaper, of any type, is very taste specific. No two people are generally going to like the same pattern of wallpaper - no matter how nice it may be; it is just too taste specific. So I recommend keeping it simple, with a solid with texture.

Post some pictures. Maybe there will be ideas to include the wallpaper. Frankly I would do it in a heart beat. These new wallpaper are great for stuff like that. I know some say don't because it would be a headache for the new owners but frankly if you are buying an older home you have to expect this stuff. I found out 3 years after buying our older home that the old owners had painted over wallpaper in one of the bedrooms. GO FIGURE. I just painted it again. Oh well.

Please do not use any type of wallpaper over another wallpaper. Remove the old. If walls are in good condition, you are better to paint, than wallpaper, since you want to sell. Buyers look at wallpaper, and think about all the work, they have to do to remove it.

You may regret papering if the results are not great and then you’ll will be in a worse situation; as well, peel and stick is harder to adjust when laying. With finicky cutting and the precision required in a bathroom when applying, it will be a pain.

Suggest instead a textured paintable paper which does a great job covering imperfections. I used on an extremely imperfect wall and it was a life saver. (Used a grasscloth pattern vs something ornate.)

https://inmyownstyle.com/adding-textured-wallpaper-called-anaglypta-to-the-dining-area.html

Wallpaper "might be" stylish in your opinion OP, but it's also very taste specific. Either make the repairs to the current paper and leave it, or take it down and paint a neutral color.

If I was looking to buy a house today, I'd see the wallpaper and immediately plan to remove it. Contrary to HGTV shows, houses do not need to look like they were featured in an interior design magazine to sell. When funds are limited focus on clean to sell.

Think about the return on investment. Is the time and money spent on a hack job of wallpapering over wallpaper really worth it? A day spent removing the old paper and repairing any damage and then painting is far less expensive than peel and stick wallpaper.

For selling, when your budget is limited, focus on cleaning, repairing and tidying up the yard. Skip the new wallpaper.

Also, replace dead or dying light bulbs with bright new LED bulbs. Older houses often have a few forlorn and dusty yellowed CFLs scattered in closets and basements - the house will look much better with new LED bulbs.

Any type of texture on the walls is not appropriate to add wallpaper to. Either leave it and decorate around it or remove it and paint

"A number of other options mentioned as well, including painting over the existing paper. "

There's a special place in hell for people who paint over wallpaper. If you value your karma, don't do it. Ever. It's a quick way to turn a quick job into having to replaster the walls for the next guy.

Right up there with wallpapering unprimed walls.

DAMHIK

@freedomplace1 posted a super helpful link above - looks like it partly depends on the material of the existing wallpaper

(using ”removeable wallpaper” in your search terms could help show you more resources)

Thanks for additional info. IME, thin peel and stick wallpaper shows every wrinkle and bump underneath it. Using it as drawer liners may be okay, but it would telegraph every seam under it when used over bona fide wallpaper. Order a single roll and try it out on one of your walls. If it looks lumpy, use it to line the bathroom vanity drawers instead.

I just papered using the peel and stick and there is no way you could get it to work on an already papered wall. It would pull off the paper when you position and you will need to position it. It sticks to everything and compound corners are near impossible. If you insist on papering over use pasted paper that you can slide and position.

As someone else posted if you are selling the house I wouldn't bother with wallpaper. Would suggest painting instead. A nice neutral color would probably be more acceptable to prospective buyers than a specific wallpaper.

According to my factory's experience, it is better to take off first the existing wallpaper et then apply the Peel and Stick one

Vivawalls Viva note you commented on a one year old post. Best to check the date before posting. Sometimes those older postings crop up.

It’s possible, but it really depends on the condition and type of the existing wallpaper. If the old wallpaper is textured, peeling, or has a vinyl coating, the new peel-and-stick wallpaper might not adhere properly or could show imperfections underneath.

If the existing wallpaper is smooth and firmly attached, you can try applying peel-and-stick over it, but test a small section first to see if it sticks well. Also, keep in mind that peel-and-stick wallpaper may not be as removable if applied over another wallpaper layer. If you're looking for a long-term solution, removing the old wallpaper first is usually the better option.