I did say that it
might work (by which I meant that it wouldn't be hard to deliberately ignore the unreasonable aspects, not that it was actually reasonable).
It's unusual for sociologists to distinguish between as many as nine social classes. The only place that I recall seeing the term 'middle middle class' used is some of Mack Reynolds' books. One of my old textbooks divides the middle and lower classes into five ('upper middle', 'middle', 'upper working', 'working', and 'poor'). A comparatively recent
study of Britain divides all of society into seven classes. In all cases that I know of, the homeless are included in the lower lower class, whatever it's called.
Adding three levels below that and four above seems a little excessive.
Jack London does speak of social differences among tramps, but I don't think many non-tramps bother with the distinctions between hobos, bindlestiffs, and stumblebums.
But a generic system (or an Imperial system) would look on it in generic terms. And if one society did actually distinguish between different classes of homeless, a generic system would simply assign them all to the one class it usually used for homeless people and possibly add a footnote (
* This society distinguishes between five kinds of homeless people, designated 0.1 to 0.5.).
Hans