Which Buddhists say that there are no conventionally existent wholes, and for what reasons? Which Buddhists say that there are no conventionally existent wholes, and what's the best reason for the claim?

My "whole" I mean something more than the sum of its parts, an object that does not reduce to its parts.
Any sect of Buddhism which emphasises the emptiness of all things probably says that there are no existent wholes but some sects would say that there are conventionally existent wholes. In other words, we can only talk about their existence from a conventional perspective. 

Here's a nice description which talks about a car's existence and its emptiness


  
    You're walking through town and you get to a street where you see a car. Is there a car? Sure thing! That's why we look left and right before crossing the street, and it would be dangerous to say that "there is no car" (without further explanation).
    
    But if we take one car aside and take a closer look, there's no such thing as a car. The windshield isn't it, the wheels aren't it, the chassis isn't it, neither is the engine. What we call a car is just a bundle, a construct not only physically but conceptually.
  


It's a point which can be difficult to convey. Something is there which will hit you when you cross the street, we call this a car. On the other hand, if we take that car and dismantle it into its pieces we can not find any piece which is the essential car-like-nature.

This is the same as when we look at the self. We can investigate all five aggregates (body, feeling, perception, mental formations, consciousness) and there is no inerrant soul or "me" to be found. However, we can still talk about the "me" existing by convention.