Otdfbt

Can a planet, star or otherwise have a magnetic field that is stronger or have more range than its gravity?

Let's look at the proper magnetic force (as opposed to the Lorentz force on a moving, charged object described in @KenG's answer) on a specimen $S$ of magnetized material with mass $M_S$ as a way to try to compare. Let's arbitrarily assume it has a fixed, permanent magnetic moment $m_S$. We can't use iron because it will saturate too easily.

Then let's look at how the forces scale differently with distance

$$mathbfF_G = -fracG M_S Mr^2mathbfhatr tag1$$

$$mathbfF_B =nabla (mathbfm_S cdot mathbfB(mathbfr)) tag2$$

If we reduce these to scalar equations at a radius $R$ (assume $mathbfm_S$ and $mathbfB$ are parallel) assume all forces are attractive, and evaluate the potentials and their gradients on the equator of the body at it's physical radius $R$. Since the magnetic force on our dipole specimen drops off faster than the gravitational force, we have to evaluate the two at the closest physically possible distance:

$$F_G = fracG M_S MR^2 tag3$$

$$F_B = frac3 m_S B_r=RR tag4$$

where our specimen is a distance $R$ from our field source, and it's moment $m_S$ is a magnetization of 1 Tesla times the volume of a 1 kg rare earth magnet, about 0.000125 cubic meters.

All MKS units, all rough, ballpark numbers with emphasis on strongest magnetic fields

Body R (m) M (kg) B(r=R) (T) F_G (N) F_B (N) F_B/F_G
Earth 6.4E+06 6.0E+24 5.0E-05 9.8E+00 2.9E-15 3.0E-16
Jupiter 7.1E+07 1.9E+27 4.2E-04 2.5E+01 2.2E-15 8.8E-17
Neutron Star 1.0E+04 4.0E+30 5.0E+10 2.7E+12 1.9E+03 7.0E-10
Magnetar 1.0E+04 4.0E+30 2.0E+11 2.7E+12 7.6E+03 2.8E-09

So even for a Magnetar (see also 1, 2) a kind of neutron star with a very strong magnetic field), the magnetic force on our 1kg specimen of permanent magnet is only 3 parts per billion as strong as the gravitational force.

You might see a much more favorable ratio if you compared two subatomic particles at short ranges (e.g. 1E-15 meters) but for astronomical objects, gravity seems to win smartly.

It depends on what object it's acting on. There are many objects, including stars, that have magnetic fields where Lorentz forces on charged particles like electrons and protons are stronger than the gravitational force on them.

Also remember that the strength of the Lorentz force depends on the speed of the particle moving through it, so a fast enough moving electron even here on Earth will receive a larger magnetic force than a force of gravity. This is how the Earth's magnetic field is able to contain charged particles in the Van Allen belts that its gravity could not contain.

It isn't impossible, but the short answer is "no".

A gravitational field will accelerate all matter and energy equally while a magnetic field will only accelerate moving electric charges (other magnets).

The force due to gravity is proportional to the inverse square of the distance, and the force due to magnetism asymptotically approaches the inverse cube of the distance. At some critical distance the gravitational force will become stronger than the magnetic force.

Unless most of the large body was magnetic, even over the magnetic poles the magnetic field would probably be too low to levitate a typical magnet in the large body's gravitational field.