Going from memory, I’m inclined to say the concept of class in Marx’s writing, at least in his later work that most fully develops his critique of political economy, is defined by the sale of labor power. The working class supply commodified labor power to the labor market. This isn’t a group of individuals: the working class is not the name for the set of individuals who do that selling (so ‘working class’ doesn’t just mean ‘all the employees’). Rather the working class is the population whose money mostly comes from the sale of labor power and who, as a whole population, produce, maintain, and bring to market commodified labor power. Within that the population there are lots of divisions and tensions, because the processes through which labor markets are ‘stocked’ with labor power are conflict-prone.
I think this all implies that politicking across class lines always involves/requires some politicking within the working class - to make one kind of conflict possible can require other kinds of conflict, to engage in one kind of conflict can bring about other kinds, outcomes in some kinds of conflicts can create, influence, defuse, or otherwise act on other kinds of conflicts. I’m inclined to say this also means that experiences of class are often only at most widespread rather than universal within the class, though really I think universality is underdetermined and politically produced: whether or not people have the same experience is at least in part a matter of how people interpret that experience. Likewise interests, when meaningful things with effects in the world, are constructed rather than given. This means as well that whether or not collective action by working class people represents the interests of the working class is itself a kind of political project.