We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter R ξ -like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in R ξ -like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in R ξ -like gauges using transverse-like non-Abelian gauge fields.Recently, in the articles [1,2,3,4], we have proposed an extension of BRST-antiBRST transformations [5,6,7,8] to the case of finite (both global and field-dependent) parameters for Yang-Mills and general gauge theories in the framework of the generalized Hamiltonian [9, 10] -see also 13,14] BRST-antiBRST quantization schemes. The idea of "finiteness" incorporates into finite transformations a new term being quadratic in the transformation parameters λ a , thereby lifting BRST-antiBRST transformations from the algebraic level to the * moshin@rambler.ru † reshet@ispms.tsc.ru 1 group level, which has been discussed also in [15,16]. BRST transformations [17,18,19] in both the Lagrangian [20,21] and generalized Hamiltonian [19, 22, 23] quantization schemes -described by a single odd-valued parameter µ and trivially lifted from the algebraic formwith ← − s 2 = 0, in view of the nilpotency property µ 2 = 0 -have first been suggested in Yang-Mills theories for fielddependent parameters in [24,25]; see also [26,27]. The introduction of such transformations is based on a functional equation for the infinitesimal parameter, providing the invariance of the integrand of the vacuum functional (in the path integral representation based on the Faddeev-Popov rules [28...