can a state machine run multiple cases simultaneously?

So a basic state machine has a case structure with different cases (states) inside a while loop.

Suppose you have a case structure with 5 different cases that are independent of each other. Independent in the sense that inputs to one case do not depend on outputs from another case.

If I took this case structure and put it inside a while loop, does this mean that the cases will get executed simultaneously? Say my states are measure temperature, measure pressue, flag when some monitor output

gets above a certain value. Will these three states (assuming each resides in a different case of the case structure) will get executed at the same time?

Does using a case structure presumes that only one case can be executed at a time? Is there any fundamental relationship between the iterator i of the while loop and different cases of the case structure?