It's worth noting that the general models ELO approximates, called item response theory (IRT) models, could handle larger than 1v1. Its similar to how you mode

It's worth noting that the general models ELO approximates, called item response theory (IRT) models, could handle larger than 1v1. Its similar to how you model situations where multiple latent skills contribute to performance (multidimensional IRT). In practice, it's a way easier though to use simple stuff like averaging / constraining groups so everyone has roughly the same skill level.