Consider a universe in which leptons & quarks (every fundamental particle that possesses electric charge) all have twins with magnetic monopole charge instead, resulting in two parallel kinds of baryonic matter--electro-matter, and magno-matter. This has all kinds of weird and interesting implications; electro-particles and magno-particles occupy different quantum states, which means they are not subject to Pauli exclusion, and electrons and magnons do not statically repel each other, so bulk electro-matter can pass right through bulk magno-matter--but they both interact identically with photons, so a wall you can walk through doesn't look any different from one you can't! And just like "normal" electro-matter can form permanent magnets, magno-matter can form permanent electrets. (I may be wrong about this, but I suspect bound states of electro-nucleons and magno-nucleons would not be stable, so we don't have to worry about mixed-type atoms; there should be two cleanly separated parallel periodic tables.)
Or at least, so it seems at first glance. But, if we change as little as possible about our own laws of physics to introduce such mirror particles, does it actually turn out that nicely? If electric charge an magnetic charge are on the same footing fundamental-particle-wise, what else necessarily has to change to keep the laws of physics consistent?