Is there any negative mass in the universe? Well, none that has been observed. But it is certainly considered theoretically possible, now.
And interestingly, at first blush, as you are thinking, you would think that + and - mass would work just like Maxwell with a minus sign. Like masses attract, while opposites repel. Well, the Equivalence Principle and General Relativity have something different to say about that. It gets very weird.
Negative mass must have negative inertia. And that means, you get another minus sign. Positive mass will attract all mass, both positive and negative, and negative mass will repel all other mass, positive included.
With Newton, that would mean that if you placed two equal and opposite masses some distance apart, they both would accelerate off, maintaing constant distance between them. That's just, well, weird. Doesn't violate any conservation laws, but is just plain weird.
Now, that's Newton. Do some General Relativity, and that situation leads to a type of "warp drive". Only problem is you need several solar masses worth of negative mass.
Now, it used be though that negative mass-energy was just impossible, but quantum theory is saying it might not be some impossible.
-Richard