Almost Lie solvable associative algebra varieties of finite base rank

For arbitrary elements $x_1,\ x_2, \ldots$ from an algebra we put $V_1(x_1,x_2) = [x_1,x_2]$ where $[x_1,x_2]=x_1x_2 - x_2x_1$ and define inductively
$$V_n(x_1,\ldots, x_{2^n}) = [V_{n-1}(x_1,\ldots x_{2^{n-1}}), V_{n-1}(x_{2^{n-1}+1},\ldots x_{2^n})].$$
An algebra or a variety of algebras is called Lie solvable if it satisfies the identity $V_n(x_1,\ldots, x_{2^n})=0$ for some $n$. Let $F$ be an associative commutative noetherian ring with $1$. In the set of varieties of associative $F$-algebras we find all almost Lie solvable varieties of finite base rank.