Ok, I just tried with the Alto household first, on the 2nd floor of their house.
All three burners fit just fine, lit and unlit.
Then I went to the Crumplebottom household, on the 1st floor of her house.
I could only fit 2 burners on at any given time, no matter what order I placed them in, no matter what order I used to place them (China 1st, Egypt 2nd, France 3rd; France 1st, China 2nd, Egypt 3rd; etc).
I also tried the "half square to half square" and the "whole square only" for Agnes, no change, the 3rd burner was not placeable.
I've not the time tonight to do more extensive testing, but I can do so later, or someone else can do it.