Yes demagnetizing is a partial thing.
The magnetic anisotropy is typically unidirectional for high coercivity magnets, meaning that the magnetic moments like to point into either of two directions on one axis.
When these magnets are sold, they are prepared such that almost the entire material has the moment aligned in the same direction. If you heat it beyond its Curie temperature and cool it back down, the orientation will be random (demagnetized). But anything in between are stable states, too, e.g. 50% of the material being aligned and 50% being randomly aligned. That way, the strength, i.e. external field will be reduced.
Aligning it at room temperature is probably futile, but the higher you warm it, the lower its coercivity will become (reaching ~0 at the Curie temperature). So if you can heat and apply magnetic fields, just play a bit. If you accidently completely demagnetize it, it is rather easy to remagnetize even with small field as long as you apply them while cooling through the Curie temperature.
Another way to reach partial magnetization would thus be to completely demagnetize it and cool it with a field which does not permeate the entire piece, leaving part of the material unaligned. But the field will not be uniform then.
A third strategy, suggested by Andy in comments, is too coat the magnet with a soft-magnetic material, e.g. iron powder or iron foil. The coating will provide a low-reluctance path that some of the flux will take, reducing the amount of flux that goes into the "far field".