Yes you can, but it leaves many questions unanswered, leaves two layers of deteriorating flooring under your expensive new floor, and means you have a less-than optimal nailing surface for the new flooring.

What kind of additional subloor or layer is needed?
Can't answer that question until you can answer these questions:

What kind of subfloor is under the 2 layers of old flooring?
How thick is the subfloor?
Are there any damaged bits of subfloor that need to be replaced?
How far apart are the joists?
Is the subfloor properly nailed to the joists over the entire floor?

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Asbestos in a flooring tile is "encapsulated". It's held into the tile by the stuff that makes tile stick together. Standard removal tools and techniques (mostly warm then up and scrape them off) are safe.

Unless you sand the tiles off, grind them to a powder and inhale the dust, or do otherwise really strange things, very little of it is going to become airborne.

Those people who got cancer from asbestosis were almost entirely people who worked with asbestos. They were mining it, spraying it, manufacturing things with it in the pre-protective gear era. They were exposed to more asbestosis in an hour then you would be if you removed the flooring yourself. And almost all of them were also heavy smokers.

If you do, I would research having an underlayment laid on top. You don't want to end up with a squeaking sound if there is movement, rubbing against the synthetic floor. Don't know how feasible this is for your application, but they do make underlayments, so I would check it out.

Would also be wondering if the wood would be able to breathe as necessary with a layer of plastic flooring underneath.

This post was edited by snookums2 on Mon, Aug 5, 13 at 13:50

Thank you. I have a lot to consider now...When they took the old cabinets out all that was under them was a thin layer of asbestos tile and what appeared to be an old wood floor. In the other rooms downstairs we have maple floors. Part of the house was built in 1870 and part in 1930. There appears to be two layers of sheet vinyl on top---one we had put down 15 years ago.

Will people who install floors look at the joists?

Thanks so much!

We had a 1880 house which came with old linoleum, vinyl, and stopped looking past those layers. We decided to pour leveling compound only over the uneven areas and installed tongue groove pre finished cherry hardwood flooring on top of a recommended flooring paper(came like a roll ). The hardwood floor was machine stapled together according to manufacturer specifications. We lived there for 6 years and the floors seemed fine with the 4 northern seasons. We didn't use any glue and installation was not easy (some tongue - groove would crack break) we did it over a few nights after work. I dont think anyone would ever notice all the layers of old floor underneath. Hope this helps.

If the wood subfloor under the layers of vinyl is sound, you should be able to lay a floor over top and nail right through the vinyls into the wood subfloor.
The wood floor installer will not look at the joists unless he has x-ray vision or it's exposed underneath.
Do not do as the commenter above did and pour a leveling compound over any part of the vinyl. Over time it could break up and start sounding crunchy.
Presumably the subfloor below your vinyl is sound enough to support a vinyl floor so it should suffice to nail a wood floor into.

You are correct, the concrete leveling compound may become crunchy over time but the old floor was uneven. We even used the leveling concrete in an area that we covered with underpad+ carpet. Nothing was straight in that 1880 house LOL. It was challenging to install anything that was straight against any wavy wall, wavy ceiling, wavy floors ( even after contractor building engineer put in basement support steel columns.) There was no way we were going to rebuild that entire 2 story 1880 home ;)

I'm probably overly cautious on certain issues since I would have to fix problems with a floor that I installed. There is one thing one can use to fill depressions on a wood floor that you're going to nail through. It's Bondo. They sell it in 32oz. cans at Home Depot. It sticks well and is flexible so there's little chance of it breaking up if the floor moves a little.

What type of cementitious floor leveler would you use to level a wood subfloor for nail-down installation?

I'm rather cautious since I'm the fourth generation in this company. I worry that something could come back and bite me, even if years have passed and there may be other factors involved.

I understand the sense of caution. Callbacks are not good and can eat away at your profits.

To answer your question: I have used products supplied by flooring distributors, and have included products from Ardex, Mapei and Fritztile. They were all used with an appropriate primer to facilitate bonding to what they were placed over. Additives were included to make the product less-likely to break apart and powder. I especially like Ardex SDP (Self Drying Patch)...because the PSI (pounds per square inch) rating is lower than some other products. Self leveling formulations can achieve a very high PSI and can be very difficult to nail into, even with pneumatically assisted fastening tools. When I used a product with a high PSI, I sometimes would have to drill pilot holes and manually drive in hardened spiral flooring nails.

I never had a floor patch crumble. I figured...if I used a good patch, and if the substrate was well-fastened and didn't move much, I believed the installation would be OK. I believe that you have to have significant movement to get a decent patch to fall apart under a finish product. I came to wood flooring out of a family business that specialized in resilient flooring materials, so I learned a lot about what you can and cannot do regarding floor patches and their application.

I will say in closing here (for general consumption) , especially for the DIYer,... if you try to use calcium carbonate patches (usually white in color...and I won't mention brands) ...you will experience quick breakdown of the product, because they are fragile and will crumble easily. If it looks like plaster of paris, it is not a suitable floor filler or patch...my opinion.

Thanks Glenn.
I mainly use Ardex products, SDP, K15 and Feather Finish, depending on the application.