A sequence \(\{{\mathcal U}_n : n < \omega\}\) of families of open sets of a topological space \(X\) is called a strong quasi-development for \(X\) if for every \(x \in X\) and for every open neighbourhood \(V\) of \(x\) there exist an open neighbourhood \(W\) of \(x\) and an \(n < \omega\) such that \(x \in \bigcup \{U : U \in {\mathcal U}_n\}\) and \(x \in \text{St} (W, {\mathcal U}_n) \subset V\). It is called a quasi-development of order 2 for \(X\) if for every \(x \in X\) and for every open neighbourhood \(V\) of \(x\) there exists an \(n < \omega\) such that \(x \in \bigcup \{U : U \in {\mathcal U}_n\}\) and \(\text{St(St} (x, {\mathcal U}_n), {\mathcal U}_n) \subset V\). In 1974 it was shown by \textit{C. E. Aull} that a topological space \(X\) has a \(\sigma\)-disjoint base if and only if it is quasi-developable and hereditarily screenable [J. Lond. Math. Soc., II. Ser. 9, 197-204 (1974; Zbl 0295.54023)]. In this paper it is shwon that the following conditions are also equivalent: (1) \(X\) has a \(\sigma\)-disjoint base. (2) \(X\) has a strong quasi-development. (3) \(X\) has a quasi-development of order 2. Additionally, spaces with a \(\sigma\)-disjoint \(\pi\)-base and almost countably subcompact spaces are characterized.