We show that the coupling of a two-dimensional order parameter to a field that breaks the symmetry of a uniaxial crystal splits the superconducting transition, leading to two superconducting phases in zero field. The high-temperature superconducting phase is one-dimensional and exhibits the broken symmetry of the symmetry breaking field (SBF) while the two-dimensional low temperature phase spontaneously breaks time-reversal symmetry. We calculate the specific heat jumps at both transitions. We show that Hc1(T), a probe of the zero field phase, displays an abrupt change in slope at the second transition. Moreover, a kink in Hc2(T) occurs for fields in the basal plane reflecting a finite field phase transition. For an SBF fixed to the lattice, the symmetry of Hc1(T) and Hc2(T) is broken in the basal plane. The observation of all three of these features, whether intrinsic or induced by external means, on the same crystal with uniaxial symmetry would provide convincing evidence of unconventional superconductivity. Our results are in qualitative agreement with recent measurements on different samples of the heavy electron system UPt3. We find that sizeable strong-coupling corrections are needed to explain the magnitudes of the heat capacity jumps and the splitting of the transition in some samples. Comparison of the discontinuity in the slope of Hc2(T) with the data of Taillefer et al. (on a different UPt3 crystal) leads to SBF couplings in qualitative agreement with those inferred from the heat capacity data. More recently, a kink in Hc1(T) has also been observed. A quantitative comparison with specific heat and critical field measurements on the same sample would provide a stringent test of this model for UPt3.