A process for fractionating the constituents of a solution obtained by extracting plant or animal material with an aqueous-organic solvent where the aqueous-organic solvent is a mixture of water and a water-miscible organic solvent, generally including the steps of contacting the solution with a near-critical fluid to produce a raffinate phase containing high polarity constituents and water, and a near-critical fluid phase containing low to medium polarity constituents, separating the near-critical fluid phase from the raffinate phase, and recovering the low to medium polarity constituents from the near-critical fluid phase and the high polarity constituents from the raffinate phase.