A multireference state formalism for determining the functions for the modified embedded atom method (MEAM) is developed. This formalism eliminates almost all of the prior arbitrary choices in the MEAM function determination and replaces it with first-principles calculations of the MEAM electron densities, embedding energy, pair potential, and angular screening functions. The formalism accepts any level of first-principles information and is applicable to all elements. It may be considered as a physically based interpolation of the first-principles data for systems that fall within the range covered by that data. The critical addition of multiple reference states includes the energy/volume relationship for those reference structures as well as reference paths connecting the reference structures. The formalism is applied to Cu as a model material. Extensive predictions of the model are made and compared to additional first-principles calculations, results of two literature EAM potentials, and experiment. Our model, which uses as input only the first-principles database, represents the first-principles calculations extremely well (better than the EAM calculations). Furthermore, it agrees with experiments almost as well as EAM models, derived from a combination of first-principles calculations and experiments.