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Consider boundary value problems for a functional differential equation $$\left\{\begin{array}{cc}{x}^{\left(n\right)}\left(t\right)=\left(T^{+}x\right)\left(t\right)-\left(T^{-}x\right)\left(t\right)+f\left(t\right),\hfill & t\in [a,b],\hfill \\ lx=c,\hfill \end{array}\right.$$ where $T^{+},T^{-}:𝐂[a,b]\to 𝐋[a,b]$ are positive linear operators; $l:{\mathrm{𝐀𝐂}}^{n-1}[a,b]\to {ℝ}^n$ is a linear bounded vector-functional, $f\in 𝐋[a,b]$, $c\in {ℝ}^n$, $n\ge 2$. Let the solvability set be the set of all points $({𝒯}^{+},{𝒯}^{-})\in {ℝ}_2^{+}$ such that for all operators $T^{+}$, $T^{-}$ with $\parallel T^{\pm }{\parallel }_{𝐂\to 𝐋}={𝒯}^{\pm }$ the problems have a unique solution for every $f$ and $c$. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl,...