Let \(M\) be an \(R\)-module over a commutative ring with identity. A family \(Q=\{ Q_1,\dots,Q_{2n}\}\) of subsets of \(M\) is called an ordering of level \(n\) on \(M\) if: (1) \(M\) is the union of \(Q_1,\dots, Q_{2n}\); (2) \(Q_i+Q_i\subseteq Q_i\) for \(i=1,\dots,2n\); (3) for all \(i \neq j\), \(Q_i\cap Q_j=P\), a fixed prime submodule of \(M\); (4) \(R\) admits an ordering \(F=\{P_1,\dots,P_{2n}\}\) of level \(n\) such that \(P_i\cdot Q_j\subseteq Q_{i+j}\) for all \(i,j=1,\dots,2n\), and for all \(i\neq j\), \(P_i\cap P_j=\{r\in R\mid rM\subseteq P\}\) letting \(Q_r=Q_s\) whenever \(r\equiv s{\pmod {2n}}\). The concept of ordering of level \(n\) for commutave rings with identity was defined by S. M. Barton [“The real spectrum of higher level of a commutative ring”, Can. J. Math. 44, 449–462 (1992; Zbl 0766.13005)]. The paper under review studies orderings of level \(n\) for arbitrary \(R\)-modules \(M\). In particular, the follwing is shown: (1) \(M\) is necesarily a semireal module; (2) \(M\) admits an ordering of level \(n\) if and only if \(M\) admits an ordering of level 1; (3) if \(M\) is finitely generated then \(M\) admits an ordering of level \(n\) if and only if \(M\) is semireal. Finally, a theorem of R. Berr [“The intersection theorem for orderings of higher level in rings”, Manuscr. Math. 75, 273–277 (1992; Zbl 0758.12003)] is generalized to \(R\)-modules.