How to get super strong magnetic force!

To obtain a magnetic force amplifier, you do not need to add a magnet for this. I suggest this option. It is necessary to make the end of the magnetic core sharpened to the required area. It does not necessarily have to be a point, I for example made a kind of strip. Better, of course, that the shape was close to the circle, the coefficient will tend to the maximum.
The first sharpening of the end.
The second magnetic circuit must be closed. You can use the horseshoes again, the ring is more profitable.
The third is that it is not necessary to use an electromagnet, you can do with permanent neodymium magnets. In such a case, the magnets will be in the middle of the magnetic circuit, and at the ends there will be pointed tips made of ferromagnetic material.
Fourth, the distance between the ends should be minimal, in order to maximize the strength of the magnetic field.

Why cut the ends. Since the magnetic properties propagate along the path of least resistance, they will tend to propagate along the magnetic circuit rather than the medium around the magnetic circuit, which has much less ferromagnet properties. By sharpening the magnetic core, we increase the density, consequently the force per unit of the port is also increased.

This can be useful for experiments or research.