Max Tegmark is perhaps the best example, with his idea which basically proposes that every mathematically possible universe exists.
Are there any other examples of physicists with a similar line of thought (preferably living physicists)?
Tegmark is only a mathematical Platonist and not a full blown Platonist and hence not a Platonist at all given how important a role the forms of the Good and the One play in Plato's philosophy.
One Einstein quote says his god was Spinoza's god. As Spinoza simply presented Platonic philosophy in geometric form, one can say that Einstein was a Platonist.
Newton, pushed away from the Trinitarianism of his time. As he also said:
Plato is my friend, Aristotle is my friend but truth is a greater friend.
One can state he was acquainted with Plato's phikosophy. This coupled with the fact he was a avowed Unitarian suggests that he was a Platonist.
Feynman in one of his later writings, The Meaning of Everythimg, appeared to endorse Christianity and given his interest in philosophy and the Platonist inflection of Christian philosophy may have endorsed Platonism.
Platonism, the acceptance of the “reality” of abstract objects, is not a widely understood question outside philosophic circles, so explicit statements by physicists will be rare to find.
An oblique way to ask the question is whether they accept that matter is primary, or math. And if one does that, most theoretical physicists are either platonists or idealists. A significant number of theoretical physicists think that physics reduces to math. And if that is true — math would be the substrate for everything, which is a very platonist view.
Additionally, the motto of many quantum physicists, and most of those that advocate for the majority Coopenhagen interpretation of QM, is “shut up and calculate”, IE do the math, that is all that matters, any further speculation or theorizing about what the math MEANS is unneeded! Because doing the math is all the meaning there is.
Additionally, any advocate of B theory of time, and treating the present and causation as illusions, is treating math as primary over experience and evidence.
I have one quote to offer, from physicist Sean Carroll, who was asked what reality is:
“The best answer we can give is that reality is a vector in Hilbert space. This is the technical way of saying that reality is described by a single quantum mechanical wave function.”
Carroll is both a platonist and an idealist, and an advocate of scientism, the reduction of everything to physics.