This is a complicated discussion, but for any given "technology" (i.e. set of available methods for producing every good/service in a society) and set of preferences among agents (e.g. households, firms) it is generally the case that there are many possible profit rates and wage schedules that allow for equilibrium.

For a very formal an influential discussion of this, see Sraffa's "Production of Commodities by Means of Commodities".

Historically, an idea closely related to the one you are articulating has been known as the "iron law of wages".

https://en.wikipedia.org/wiki/Iron_law_of_wages