In this paper, we introduce and analyze the notion of disjoint $(m_{n},i)$-distributional chaos, where $1\leq i\leq 12,$ as well as the notions of disjoint $m_{n}$-distributional chaos of type $2$ and disjoint reiterative $m_{n}$-distributional chaos of types $1+$ and $2^{Bd}$ for general sequences of multivalued linear operators in Fréchet spaces. We reconsider and slightly improve our recent results regarding disjoint distributional chaos in Fréchet spaces.