This work addresses the thermodynamic limiting behavior of dilute species in bingry solutions as described by their excess chemical, mechanical and thermal partial molar properties (M) over cap (E)(i) (TPx(i)) as well as the corresponding composition slopes [partial derivative(M) over cap (LR)(i) (TPx(i))/partial derivative x(i)](TP), where (M) over cap (LR)(i) (TPx(i)) comprises the partial molar properties of systems describing the excess Gibbs free energy and the corresponding temperature- and pressure-derivative quantities. These quantities include the species partial molar Gibbs free energies according to Lewis-Randall (LR) description, and their volumes, enthalpies, entropies, and isobaric heat capacities. The analysis builds upon the recently proposed solvation formalism for dilute systems [J. Chem. Phys., 128 (2008); J. Chem. Phys., 148 (2018); Fluid Phase Equilib., 472 (2018)] and its scope includes (a) the identification of the microstructural signatures, macroscopic manifestation, as well as the interrelations between the species partial molar quantities (M) over cap (LR)(i) (TPx(i))[partial derivative(M) over cap (LR)(i) (TPx(i))/partial derivative x(i)](TP), and the apparent molar counterpart M-phi(TPx(i)) at finite composition as well as at infinite dilution; (b) the development and testing of a method to describe the actual limiting (M) over cap (LR)(i) (TPx(i) -> 0) behavior in terms of the corresponding value at the condition of solute saturation, i.e., (M) over cap (LR)(i) (TPx(i) = x(i)(sat)); (c) the illustration and discussion of some successful approximations for the accurate estimation of the limiting (M) over cap (LR)(i) (TPx(i) -> 0), and consequently, (d) the discussion of potential drawbacks underlying the composition regression of experimental data and subsequent extrapolation to infinite dilution. (C) 2019 Published by Elsevier B.V.