If you need to build some grand pantheon to say from on high "these are the social classes", you've already failed. Social distinctions exist around interests which can be held, rather than ideas of what a "class" is supposed to be. The interests and institutions in any society are not a mystical thing. If they are large enough to be relevant, their impression will be known to everyone in the society. No amount of secrecy and conspiracy can hide an interest that seeks to command the world, and interests always have definite origins rather than ideological ones. The nobility held land and armies, and forbade the lower classes from any form of self-defense. That is what aristocracies do as a matter of course, however they are constituted.
Very large and singular loci of wealth, like large banks, constitute interests in of themselves, where the class that truly commands them in very small. The idea of a class as some hive mind has never truly existed. It is an ideal of philosophical republicanism, but in practice the republics are rife with infighting at the very top, which is reproduced all the way down to the lowest classes. Republics are maintained by fear and loathing from their foundation, and the imagined virtue of a republic is always a myth. Where the virtue actually exists, it has always been understood to exist in men, rather than in the idea of a republic itself. If the men are so vile that they would rather cannibalize anything good than cooperate even at a basic level, the republic becomes such a disaster that its removal will be most welcome. If you wanted cooperation, it would only be possible through men choosing it. No force in nature or mankind will compel cooperation, let alone insist that it is inevitable. Such theories are inherently inclined towards republican fascism, which is always a clusterfuck and the ruin of all contending interests.
So much stupidity involves keeping up the myths of a republic, which were never believed by the founders of the modern republics, nor were they believed by ancient republicans. It was always understood that republics were a compromise because no one could be a king, rather than an ideal for their own sake. That ideology was for the slaves. Those who rule in a republic have always known it was all a lie, and brag about how easy it is to keep the soldiers marching and killing like retards. They can get them to do anything for Fake Jesus.
To make any useful class analysis, you ask a few simple questions about what people do. That is why the first analyses of class society in Antiquity saw the division of labor as the origin of distinctions, rather than any essence of people or a conceit about what people are supposed to be. In actuality, the class distinctions concern the functions that a class executes, rather than the men themselves. Men are beholden to these functions in order for the society to remain constituted, and all of these functions focus on locuses not just of individual men but the machines and structures they build. It's difficult to be a powerful institution without some real estate and a building, perhaps a temple, to call yours.
The technological and intellectual interest, centered around the universities, is very clearly the leading interest. This interest decides who enters the formal institutions of the state, decides what you can and cannot be in any area of employment, and is joined with the highest levels of capital. The aim of every competing faction is to control this institution or ensure they have a seat in it. Gramsci's strategy explicitly calls for this. The fascists and Nazis placed these institutions at the apex and staffed them full of fanatical loyalists. The liberals rule because they command intelligence, knowledge, and insinuate that through this they can control reality itself. The money is secondary to the function of commanding people intellectually and controlling their behavior in minute ways. Those who command the banks long ago saw that it was through science, technology, and the command of education that they would best rule. The capitalists who embraced this are the capitalists who were able to win capitalism, and have been winning for the past century. We know who won capitalism, and so much effort is spent pretending that those who win didn't win or somehow didn't exist at all. It's all mystification.
With the rise of technocracy, the old bourgeois/proletarian distinction lost relevance. The rise of technocracy is, for the most part, the victory of the bourgeois classes, which transformed into technocratic classes and managers and co-opted those of the proletarians amenable to such a world. The Nazi intellectuals at the end of the war made it clear that the result of the war had been that the bourgeois system was destroyed forever, and replaced with this thing that they cleverly obfuscated through mystification as soon as the war was over. The only people who believe in this fantasy version of class struggle are the desperate who need to believe the struggle is something other than it actually is, and that is why there is a left that habitually fights the battles of the past symbolically - because they long ago conceded that they only exist to win a seat in the new system, and didn't need the workers for anything. There is a left that understands the fallacy of this, but that part of the left has been defeated over and over again. Many who held to that faith died, committed suicide, or just gave up and accepted it was over a long time ago. All that remains is this rump of grifters that is Johnny on the Spot to kick down anything that would actually resist what rules the world, and a few intellectuals bemoaning what has become of the human project.
A true "class analysis" would require accepting the centrality of eugenics, which all of you refuse absolutely to acknowledge. To acknowledge it requires you either believe the victory of eugenics is a fait accompli, or requires you to resist every institution active today. If eugenics is truly natural, then there is never any reason to believe there can be a revolution or any change at all, and all life dies screaming forever. We know what eugenics stands for and they brag that they will make the world into a torture chamber.
The command of money is pointless when the money is fake and those who rule can print however much they like. Money is nothing but a tool to control the lower classes. The rich converted their wealth to that which will allow them to rule in the successor system, and always kept much of their wealth in some assets which were useful for ruling. The fetish for money is never as absolute as Marx claims. Most who contend for power in capitalism were not convinced that money was a fetish object at all, and that is where Marx engages in some mystification. He had to do this to sell his idea at the time, because stating bluntly what his program entailed would mean (a) it would reveal the interest Marx was actually for, which was not the workers, and (b) it probably would lead to the suppression of his work if he acknowledged too frankly what was to be done, so he expected readers to get the hints he was dropping. It's why Marxists have been habitually hostile to those who don't have an inclination to buy into his wonky thinking about humanity and society.