The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multi-level design approach to deal with the issue of designing large neighborhood based operators. The main idea is inspired from stacked generalization (a multi-level classifier design approach) and consists in, at each training level, combining the outcomes of the previous level operators. The final operator is a multi-level operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperforms the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multi-level approach to obtain better results.