  We construct an efficient parameterization of the pure neutron-matter
equation of state (EoS) that incorporates the uncertainties from both chiral
effective field theory ($\chi$EFT) and phenomenological potential calculations.
This parameterization yields a family of EoSs including and extending the forms
based purely on these two calculations. In combination with an agnostic inner
core EoS, this parameterization is used in a Bayesian inference pipeline to
obtain constraints on the e os parameters using multi-messenger observations of
neutron stars. We specifically considered observations of the massive pulsar
J0740+6620, the binary neutron star coalescence GW170817, and the NICER pulsar
J0030+0451. Constraints on neutron star mass-radius relations are obtained and
compared. The Bayes factors for the different EoS models are also computed.
While current constraints do not reveal any significant preference among these
models, the framework developed here may enable future observations with more
sensitive detectors to discriminate them.
