Is a classless society possible?
Marx suggested it is under communism.
It seems that his idealism exceeded the bounds of the attainable.

In a totalitarian society, virtually everyone could be forced to into one social class. But there would still have to be a group ruling the society, this could be considered the "ruling class." Since all the people in a society would not likely agree to remain in the same "class" voluntarily, because many would tend to strive to better themselves, it appears to me that the notion of a "classless" society is not feasible.

American institution of social sciences

Marx suggested that the natural progression of history would result, ultimately, in a society in which the workers would own the means of production. In this world, everyone would be a worker, and everyone would be an owner. This vision is actually quite reminiscent of what the contemporary affluent West looks like. We work for a living, and much of our income is invested in 401ks or pension funds or investment accounts, making us partial owners or stakeholders in the means of production. In this way, contemporary consumer capitalism in the liberal West resembles what Marx and Engels described as 'Communism' far more than the Leninist projects in the East.

The missing link as to why the 'Communist' USSR was a brutal tyranny and the USA is a real worker's paradise lies in the fact that Karl Marx would have been appalled at Lenin's suggestion that an elite 'Vanguard party' ought to be able to do whatever it deemed necessary to lead the ignorant masses to a glorious 'Communist' future. Lenin wanted power first, not social justice. Power was the means and the ends, and social justice would be secondary. Power, as has been noted by historians, tends to corrupt, and did.

In the USA and the greater liberal West, democracy allowed the people to discuss amongst themselves how and what would be the best path to prosperity. This dialogue that can take place in free societies is what Marx described, and extrapolated to be the historical dialectic that drives material progress.

I say Marx was right about the basic principles, and got some details wrong. There is much debate among contemporary philosophers about how Marx would react to social conditions he never lived to see.

The Leninist reading of Marx led to some brutal tyranny in the name of Progress, and that's why one ought to think critically when one hears another arguing for "change" or "progress" in an effort to gain power.

A classless society is impossible. Marx must have been deranged. It troubles me that Marx is considered an 'idealist'; obvioulsy, some weak intellects (not you; I mean professors and journalists, etc.) lack the ability to assess and discern.