There's a product out there called DIF by Zinsser that's used to help w/this job. (There's a home remedy which someone may offer to you here on the Forum but I've never tried it.) Anyway, you'll need to purchase a Paper Tiger too from the Home Center or the Wallpaper Retailer. The Tiger is a toothed-wheel that you use to 'cut' through the wallpaper with. You ONLY press hard enough so the teeth of the Tiger just 'touch' the wall underneath. If you press too hard, you'll perforate the wall and have a NEW problem to fix!
Since you have multiple layers, try peeling off the top what you can with the steamer until you get down to 1 or 2 layers. This should go quicker than trying to get all 3 off at once. Then, once you get to the 1 or 2 layers, work with the Tiger and the DIF. Follow the direction for the DIF TO-THE-T. Always have a pot of hot water on the stove (w/o trying to burn down the house of course!) Perf the paper with the Tiger, apply the DIF and wait per the instructions, then go at it. DO follow those instructions because if you try to rush the job, you'll only get frustrated. I also bought a carwash sponge, one of those real fat sponges, to apply the DIF with. Also, have a pair of rubber gloves on too because you'll be dipping your hands in the DIF solution which calls for HOT water. If the job is going right, you should be able to peel off the wallpaper in sheets. And don't be afraid to apply a 3rd 'coat' of the DIF if the recommended 2 isn't enough. The other problem may be that the Tiger didn't go 'deep' enough into the paper to get to the 'underside' of the wallpaper on the wall.
If you need more, post up or e-mail me direclty. My best to ya and hope this helps.