If it was me I would take out the old tile even if it is more work. This is because I would want the new tile to have a good foundation to stick to, I'd worry that the old ones would not be the best to adhere to, Plus I'd want it all even. No dents or grooves. Plus some older vinyl yellows over time and I'd worry that would bleed through eventually: (
I know it's labor intesive but I think in the long run it would last longer and look better.
My dad helped us put in new lino in our old house (bathroom) and he was very particular to cut around the edges "tight" (not to close & not to far away from the edge!!!just right) and very straight, even though we caulked around the edge where it met the moulding. It turned out wonderful.
Just my $0.02

thanks for your .02

I'm just wondering how possibly a tile underneath a new tile could possibly "bleed" through...I just dont believe that this is possible. It defies reason....These materials are not wet, (Like paint that might soften an underlying material causing it to "bleed")

any hoo...

I'd still like to hear from anyone who has successfully done it this way.

The existing floor is in perfect condition, however, I'm interested in changing the colors (hence the new tile puchase). I'm not at all concerned with an uneven surface if it were to go over what's there now.

I guess my real concern was the molding (as stated intially) and I was trying to find someone out there who might know a solution to fitting the new tile or cutting it without having to take it up and redo it.

anyone?

Of course you can lay the new on the old. A solution for the molding is to put quarter round down. A little more work but not much.

With regard to problems seeping into new tiles. This can happen. My vinyl has a slowly growing stain. In time that damage will make its way to the new product. Personally, not worth taking a chance. I would rather remove the old and put the new stuff down fresh.

There are many shows where they remove several layers of peel and stick so it is obviously something that is done by many. Whether it is proper installation or not is another question.

My dh has a saying we stick by, not trying to be rude or anything, but if you are going to do a job right, do it right the first time. Most of our jobs end up taking longer, costing a few dollars more (which I do not always have) but in the end come out beautifully.

Take the shoe molding off and fit up to the baseboard...then reinstall it or fit and install new shoe.

Fit 'net' to door trim. You can undercut these, but then you'll have a slot in your door trim should you someday remove all the flooring and install new...you'd have to make sure that the level of your new floor would meet the bottom of the slot you cut or the slot would be visible as a cut line above the flooring. I usually undercut door trim and sometimes the jamb as well to make for a neat looking job.