Could the magnetic properties of a piece of negative mass only be realized around another piece of negative magnetic mass?

I think you need to define some terms here. What is “negative magnetic mass”? I understand each of those words, but the combination into a phrase is essentially meaningless to me.

Non-magnetic is a thing, as we generally understand magnetism to be a binary thing: “magnetic” and “non-magnetic”. (I’d be willing to stipulate that the potential third state of a material in a discussion of magnetism would be “iron” or “iron-like”, in that it is attracted by magnets, even though it may not be inherently magnetic; so “magnetizable” in that sense. “Negative magnetism” doesn’t make any sense that I can comprehend. And I’m not aware of any property of mass or magnetism that relates to the other thing. That is, the strength of a magnetic field depends on the mass of magnetic material, yes, but the magnetic force is inherent in the material itself, and not in its mass.

And “a negative piece of mass” is not a realizable thing that we know of yet. Although anti-matter has been postulated, I’m not aware of its provable existence yet.

Antimatter exists and is commonly observed. Producing large amounts of antimatter or even just antimatter versions of atoms is much more difficult. Anti particles have the same mass as their normal matter counterparts, and magnetic fields produced by the motion of charged antiparticles are the same also.

Like @CWOTUS, I would also like to understand what you mean by negative mass?

Negative mass is different than antimatter. A tiny amount of a liquid with negative mass was recently created in a lab recently. I posted a question about it not long ago.

I’m not entirely sure if it’s possible for something with negative mass to also have magnetic properties though.