Vinyl Flooring Over Old Vinyl Backer

I pulled up vinyl flooring in a bathroom over an area about 4' by 8'. The top layer came off, but left a uniform backing layer firmly stuck to the floor. Can I put adhesive on this surface and apply a new vinyl flooring over it? A guy at Lowes said he didn't think it would work. He suggested I buy a chemical that soaks through the backer and softens the adhesive. I used that over hardwood in another area and the can said not to use it on particle board (it would probably dissolve the wood's adhesive). Particle board is the underlayment in the bathroom. In fact that is the reason I am replacing the vinyl flooring - the particle board fell apart under the stool. I had planned on removing the particle board, but it runs under a built in place vanity, so I am only going to take up a piece of the particle board under and around the stool - where is turned to nasty sawdust. My replacement underlayment is almost a perfect thickness match with the existing particle board/vinyl backer combination so I really need this to work. Has anyone done this? If so, how did it work?
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wrote:

I would rethink the vanity. It SHOULD be easy to remove if it was a prefab vanity like they sell at Lowes or HD... This way you'd replace all floor and be at same level, getting rid of particle board replacing with plywood. Removing and reinstalling vanity should be just disconnecting water lines and drain, and removing 2 or 4 screws securing it to the wall. (plus pulling any molding) MUCH neater job, and more apt to remove ALL of bad flooring.. I wouldn't want damp, damaged particle board left in floor.... Chuck
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