There exist several methods dealing with the reconstruction of rooted phylogenetic networks explaining different evolutionary histories given by rooted binary phylogenetic trees. In practice, however, due to insufficient information of the underlying data, phylogenetic trees are in general not completely resolved and, thus, those methods can often not be applied to biological data. In this work, we make a first important step to approach this goal by presenting the first algorithm --- called allMulMAAFs --- that enables the computation of all relevant nonbinary maximum acyclic agreement forests for two rooted (nonbinary) phylogenetic trees on the same set of taxa. Notice that our algorithm is part of the freely available software Hybroscale computing minimum hybridization networks for a set of rooted (nonbinary) phylogenetic trees on an overlapping set of taxa.