To predict the complex transient rheology of thixotropic elasto-viscoplastic (TEVP) fluids, we generalize a previous scalar thixotropic-only "multilambda" (ML) model [Wei et al., J. Rheol. 60(6), 1301-1315 (2016)] and combine it with the isotropic kinematic hardening (IKH) model [C. J. Dimitriou and G. H. Mckinley, Soft Matter 10(35), 6619-6644 (2014)]. This new constitutive equation, which we call ML-IKH model, has the following features: (1) Multiple thixotropic structure parameters that collectively exhibit a stretch-exponential thixotropic relaxation in step tests; (2) nonlinear thixotropic kinetic equations in both the shear rate or stress and the structure parameters; (3) incorporation of the Armstrong-Frederick kinematic hardening rule [C. O. Frederick and P. Armstrong, Mater. High Temp. 24(1), 1-26 (2007)] for the evolution of yield stress; and (4) viscoelasticity. We evaluate this 12-parameter model, discuss its four key features, and compare its predictions with those of the ML, IKH, and modified Delaware thixotropic models [Armstrong et al., J. Rheol. 60(3), 433-450 (2016)] for two sets of experimental data [Wei et al., J. Rheol. 60(6), 1301-1315 (2016); Armstrong et al., J. Rheol. 60(3), 433-450 (2016)] of a TEVP fumed silica suspension. The shear-rate histories include steady state, step shear rate, step stress, intermittent shear, flow reversal, and large amplitude oscillatory shear (LAOS). We show that in step tests the thixotropic and viscoelastic evolutions are dominant, while intermittent shear tests the multiple thixotropic timescales, and flow reversal tests the viscoelastic and plastic evolutions. The rheological responses in LAOS tests are more complex and involve all aspects of TEVP rheology. The four features quantitatively capture different aspects of TEVP rheology. We also provide a tensorial formulation of the ML-IKH model that is frame-invariant, obeys the second law of thermodynamics, and can reproduce the predictions of the scalar version. (C) 2017 The Society of Rheology.