Kalliope and Monopol will swap in some small sizes. Olympia and Criterion will swap if you adapt the center spindle in your machine.
Regina and Polyphon will swap in 8', 11' and 15 1/2' sizes. The discs don't swap between brands, with the following well-known exceptions: The cut of the star wheels, and the tuning of the comb, were different on each brand. What if every automobile in the world required a different size and type of tire? That's exactly the situation with disc music boxes. When collectors refer to, say, a fifteen and a half inch Regina they're talking about the size of the disc and not the size of the cabinet. These antique music boxes were made in sizes capable of playing anything from around a 5 inch disc to around a 33 inch disc.
So here's a short list: in the United States - Regina, Olympia and Criterion in Europe - Polyphon, Symphonion, Kalliope, Mira and Stella.
I won't subject you to a long list of brands it would be a little like trying to list every marque of antique automobile and although an Overland, for example, was a rugged car it's unlikely you'll ever be required to restore one. These machines, which involved little hand worksmanship, were mass produced in Germany, Switzerland, and the United States. The disc music box was introduced in the mid 1890s.