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The objective of this work is to systematically include non-Newtonian effects in a previous Newtonian model of the leukocyte and to study the effects thereof on leukocyte rheology. The standard Newtonian-drop model of the cell is enhanced in three respects: (1) The cortical layer is treated as an elastic membrane with a nonlinear stress–strain curve to simulate unfolding of the excess surface area of the membrane. (2) A power-law shear thinning fluid is used for the cytoplasm. (3) A three-layer or compound cell model is used, which is comprised of the membrane cortex, cytoplasm and nucleus. Combinations of these aspects are also investigated. The governing equations for this multifluid system are solved in the Stokes limit. The immersed boundary technique is used to simulate the interaction of the elastic membrane with the flow field. Results indicate that each of these additional elements in the leukocyte model yield significant deviations from the Newtonian deformation and recovery behavior of the leukocyte. However, the added modeling sophistication does not appear to be sufficient to fully capture all the distinctive responses of the leukocytes under a wide variety of deformation and recovery protocols. It is shown that although a comprehensive model for the leukocyte remains elusive, the three-layer leukocyte model with cortical elasticity is a promising candidate.