Scenario: multi-unit 2 story apartment, I'm the owner. People living up and down are cousins to each other and are in process of switching apts - long story, don't ask. Uppers have aready moved down but downers have yet to move up, so top is vacant for a few more weeks.

Lower unit kitchen has nice vinyl tile that's easy to clean that tenants like and are used to, while upper kitchen has commercial very low-pile carpet which helps with sound. Kids running around make reducing low-end sound a priority. Lower unit people have requested similar tile for upstairs for easy cleaning, but I don't want to get rid of carpet for aforesaid reason.

Sound on high end of scale between units is not a current problem, it's the footsteps/running thuds I would want to keep minimized, which no doubt may be higher with just tile over pine. Rest of unit will remain carpeted.

Tongue & groove pine is below carpet. There's very little "give" on the carpet. Can I sandwich the carpet in with quarter-inch subfloor, screwed down well, topped with vinyl? (This is the part where you say yes, ha.)

I may use no-glue tile or tile squares with silicone adhesive. I'm not concerned about absolute perfection in performance/looks for this. If not ok to sandwich carpet, I don't want to put down expensive soundproofing stuff and would tell the tenant to live with carpet.

Seems the only reason not to sandwich would be if a future 300lb'er would jump around cracking the subfloor, but they are all small people.