Principally all round millipedes can be kept together without issue so long as each species care requirements are met. Millipedes are not eusocial however, and do not require other specimens to survive or thrive. Keep in mind that for breeding purposes it is often best to leave the males and females of tropical and temperate species together. Species that hail from arid regions can sometimes be induced to mate if the males are removed from the females for a period of time, and reintroduced at the start of the "monsoon" season.
Sphaerotheriids can also be housed with round millipedes, though the cool temperatures preferred by some of the larger species may be at odds with the temperatures needed by the round millipedes. There are few-to-no reports of enthusiasts keeping glomerids and round millipedes together. Flat millipedes (poly-and-platydesmids) usually require a substrate that is mostly crushed rotting wood; they also exude their chemical defenses constantly, and so thus are best kept by themselves. Some high-altitude species also appreciate cool temperatures that are not favored by other tropical and temperate round species.
Whenever considering housing multiple species together be sure to research and make sure the species one has selected are not capable of hybridizing (the same goes for housing different color forms of distinct locales together). This is usually only a problem with species from the same genus or species complex, but it should be researched and considered whenever housing similarly sized species that are closely related. Many enthusiasts often ask why this is important, to which experienced breeders will answer that it is of utmost importance to safeguard the genetics that make each species unique. This may appear to be a rather esoteric answer, but one only has to look to what has happened with many of the species of hissing roach (Gromphadorhina, Elliptorhina, "Princisia", etc.) from Madagascar in both North American and European breeding circles that have now been muddled with each other to produce drab-looking hybrids that have lost all the appeal that made the original species attractive. Any and all enthusiasts/breeders should do their best to prevent the same happening with millipedes. By the same token, different localities of the same species should be kept separately, especially when the taxonomy of the species in question is doubtful, or if there is a possibility that one is keeping a species complex.
Non-millipede cage mates are generally inadvisable. Springtails (various Collembola) are one of the few exceptions and most species are to be welcomed in the enclosure, due to their useful work in eating rotting detritus and molds. One species however, cf. Sinella curisvesta, is notorious for its ability to explode in numbers and stress other invertebrates out through constant tactile stimulation (similar to issues that arise when there are grain mite outbreaks), and is best to be avoided when keeping millipedes.
Other invertebrates, such as isopods, roaches, slugs, and snails, are to be avoided due to their penchant to disturb or eat molting millipedes, cover their spiracles in slime (a problem with gastropods), or otherwise outcompete them for food. All of the above have been observed to feed on young and molting millipedes. With careful planning, and at times experimentation, it is possible to mix certain species of different groups, though if in doubt, keep them separately. Other invertebrates such as phasmids could possibly be kept with millipedes due to their disparate lifestyles, but adequately balancing the care requirements of both is often tricky.