https://www.quantamagazine.org/quantum-bayesianism-explained...
"Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance."
https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf
By the way, the "collapse of the wave function" describes as well the transition from one state to another state. I don't understand what do you mean by "multiple simultaneous states".