The time-harmonic scattering problem from an isotropic multilayer coated 3-D object is considered. The coating is modeled by an impedance boundary condition (IBC) prescribed on the outer surface of the coating. The standard Leontovich IBC is local and constitutes a poor approximation for low index materials. A possible remedy is to employ high order IBCs (HOIBCs) involving tangential differential operators multiplied by coefficients. A generic HOIBC formulation (termed here IBC3) with five coefficients is considered here. Sufficient uniqueness conditions (SUCs) are derived for the corresponding Maxwell's problem (i.e., Maxwell's equations in free-space, radiation condition at infinity and IBC3 on the surface). The IBC3 coefficients are obtained by minimizing, with the SUCs as constraints, the error between either the exact and IBC3 impedances (local planar approximation) or the exact and IBC3 Mie series coefficients (local spherical approximation). Finally, the IBC3 is numerically implemented in a well-posed EFIE+MFIE formulation. Numerical results obtained on 3D objects demonstrate the high accuracy achieved with the constrained IBC3.