We have applied a two-structure approach to the description of the thermodynamic properties of supercooled and stretched water, metastable toward vapor, ice, or both, by incorporating the stability limit of liquid with respect to vapor at negative pressures. In addition to the properties of water considered in previous studies, we include new data recently obtained in deeply supercooled and stretched regions. Our model reproduces the experimentally observed anomalies in metastable water up to 400 MPa and down to −140 MPa, and can provide a physically based extrapolation in regions where no measurements are available yet. Moreover, we are able to elucidate the thermodynamic nature of the alternative “states” of liquid water, namely, high-temperature denser water (state A) and “mother-of-ice” lighter water (state B). Based on the internal consistency of the described anomalies and new data on the isothermal compressibility, we exclude the critical-point-free scenario in which the first-order liquid-liquid transition line would continue into the stretched liquid state (doubly metastable) crossing the vapor-liquid spinodal. A “singularity-free” scenario remains an option for explaining supercooled water’s anomalies within the framework of two-state thermodynamics; however, the extreme case of the singularity-free scenario, ideal mixing of A and B, seems improbable. We have also clarified the concept of fast interconversion of alternative states in supercooled water as a phenomenological representation of distribution of short-ranged local structures.