Suppose $\Phi$ is an irreducible classical root system with simple roots $\Delta=\{\alpha_1,\ldots,\alpha_n\}$ and consider a subset $\Delta'=\{\alpha_{k_1},\ldots,\alpha_{k_m}\}\subseteq\Delta$. Given $c_1,\ldots,c_m\in\mathbb{N}_0$ not all zero such that $X=\{\sum_{j=1}^mc_j\alpha_{k_j}+\sum_{\alpha\in\Delta\backslash\Delta'}d_\alpha\alpha\in\Phi\colon d_\alpha\in\mathbb{N}_0\}$ is nonempty, say that an element $\beta\in X$ is maximal if $\beta+\alpha\notin X$ for any $\alpha\in\Delta\backslash\Delta'$, and minimal if $\beta-\alpha\notin X$ for any $\alpha\in\Delta\backslash\Delta'$. Clearly maximal and minimal elements exist, but for which root systems are they necessarily unique?
Note that $\sum_{j=1}^mc_j\alpha_{k_j}$ is not necessarily an element of $\Phi$.