Question about magnetic forces beyond saturation

Hi,

We did not cover magnetism in depth in my Year 12 Physics syllabus,
particularly what happens beyond saturation. Googling around didn't
turn up much but perhaps I am searching for the wrong terms.

Based on my understanding of gravity and electrostatics, if we
increase the field strength of one test mass or charge, the force on
the other test mass or charge increases proportionally; i.e. the
amount of gravitational or electrical potential energy we get from
moving the test mass or charge from infinity to a specified distance
doubles if we double the fixed mass or charge.

If we place a ferromagnetic material in a field sufficiently strong to
just saturate it (say 2 Teslas), and measure the force acting on it to
be F...will this force increase to 2F if the field strength it is in
is increased beyond its saturation point to say 4 Teslas?

What are the typical pull forces of modern short duty resistive and
superconducting electromagnets 1m, 2m, etc away from them?

Thanks.

Jessie xx
.

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