I put down lino squares over existing lino ALL the time and with no problem.
I never go any more than two layers, and if the existing floor or flooring underneath is comming up or broken or not adhered well, then I stop and request that all be taken up.
you have to have a sturdy and sound floor which to lay a new one on. If there is a chip in the existing flooring, (this all refers to lino squares and sheet ONLY), then apply some levelor or stick in a dummy sheet to get level.
Second, I always PUSH lino squares. The reason if something happens and one is chipped, torn or burn't, then just replace it. Sheet vino, you cannot do this, but you do have the square lines.
Third, if laying squares over squares, DO NOT line up the new tile corners and sides with the existing ones, do a one half overlap so that they become more stable.
Fourth, before you lay down tile, clean the surface well with bleach and water mixed. You want all the gunk up. I normally require the homeowner do this before I come in and lay the tile. If its not to my satis, then I do it myself.
Then finally, as you go, remove all little debris that you see or find, A small particle will make the tile stand up like it was a marble underneath and the "high" spot will wear out much faster.