You will have to take the word of a liar!! -- every piece of iron on the earth saturates as the flux increases. To make the most of the possible flux in the iron, it is usual for the iron in a machine to be in the "non-linear" part of the ampere turns/flux density graph at rated load.
This is a very difficult question to answer if you do not understand how iron and other ferromagnetic materials work to provide a higher magnetic permeability than free space. For it is the loss of permeability itself that defines saturation.
The simple explanation of how permeability works is that there are tiny atom size magnets that can be spun to align in a magnetic field inside the iron without breaking any chemical bonds that hold the iron together. When the permeable material is not magnetized the orientation of these magnets will be a completely random. When an external magnetic field gets applied some of the magnets orient themselves to match the magnetic field applied. As the applied magnetic field increases more internal magnets align. Eventually though one reaches a point that all of the internal magnets that can align are aligned. This is saturation.
This analogy is a very useful analogy for it also explains another phenomena with magnets, hysteresis. As one might imagine after a batch of these little magnets align in one direction if the external field gets removed many but not all of the magnets go back to their random alignment. This residue of magnets that retain an alignment is what is known as hysteresis.
Now why Iron and other metals do or don't present magnetic properties gets into a much deeper discussion on the nature of orbitals in atoms that is a much deeper discussion.
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"Don't disturb my circles." translation of Archimedes last words