Deformations of the antibracket with Grassmann-valued deformation parameters

We consider the antibracket superalgebra realized on the space of smooth functions on $\mathbb{R}^1$ with values in the Grassmann algebra with one generator $\xi$ and consisting of elements of the form $\xi f_0(x)+f_1(x)$ with compactly supported $f_0$. Any basis of the second cohomology space with coefficients in the adjoint representation of this superalgebra consists of three odd and infinitely many even elements. We describe a large class of deformations of this superalgebra with Grassmann-valued deformation parameters. In particular, we find all deformations of this superalgebra that have exactly three odd parameters.