The authors present a model for the superconducting states of UPt3 in which a two-dimensional order parameter couples to a field that breaks the hexagonal symmetry of the crystal. This symmetry-breaking field (SBF) splits the superconducting transition, leading to two superconducting phases in zero field. The high-temperature superconducting phase exhibits the broken hexagonal symmetry of the SBF, while the low-temperature phase spontaneously breaks time-reversal symmetry. The authors calculate the specific heat jumps at both transitions and compare with the recent measurements by Fisher et al. They find that sizeable strong-coupling corrections are needed to explain the magnitude of the heat capacity jumps and the splitting of the transition. They show that a kink in the upper critical field occurs for fields in the basal plane. Comparison of the discontinuity in the slope of Hc2(T) with the data of Taillefer et al. (on a different UPt3 crystal) is in qualitative agreement with the heat capacity data. They also predict a change in slope of Hc1(T) at the temperature of the second peak in the heat capacity, for all field orientations. Observation of all three features in the same single crystal would provide convincing evidence for unconventional pairing in UPt3 and would be a stringent test of the model presented.