  Following our recent study [P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888
(2014) 92], we discuss the notion of finite BRST-antiBRST transformations, with
a doublet $\lambda_{a}$, $a=1,2$, of anticommuting (both global and
field-dependent) Grassmann parameters. It turns out that the global finite
BRST-antiBRST transformations form a 2-parametric Abelian supergroup. We find
an explicit Jacobian corresponding to this change of variables in the theories
with a gauge group. Special field-dependent BRST-antiBRST transformations for
the Yang--Mills path integral with $s_{a}$-potential (functionally-dependent)
parameters $\lambda_{a}=s_{a}\Lambda$ generated by a finite even-valued
functional $\Lambda$ and the anticommuting generators $s_{a}$ of BRST-antiBRST
transformations, amount to a precise change of the gauge-fixing functional.
This proves the independence of the vacuum functional under such BRST-antiBRST
transformations and leads to the presence of modified Ward identities. The form
of transformation parameters that induces a change of the gauge in the path
integral is found and is exactly evaluated for connecting two arbitrary
$R_{\xi}$-like gauges. The finite field-dependent BRST-antiBRST transformations
are used to generalize the Gribov horizon functional $h_{ 0 }$, in the Landau
gauge of the BRST-antiBRST setting in the Gribov--Zwanziger model, and to find
$h_{\xi}$ corresponding to general $R_{\xi}$-like gauges in the form compatible
with a gauge-independent $S$-matrix.
