Beside its central place in FCA, the task of constructing the concept lattice, i.e., concepts plus Hasse diagram, has attracted some interest within the data mining (DM) field, primarily to support the mining of association rule bases. Yet most FCA algorithms do not pass the scalability test fundamental in DM. We are interested in the iceberg part of the lattice, alias the frequent closed itemsets (FCIs) plus precedence, augmented with the respective generators (FGs) as these provide the starting point for nearly all known bases. Here, we investigate a modular approach that follows a workflow of individual tasks that diverges from what is currently practiced. A straightforward instantiation thereof, Snow-Touch, is presented that combines past contributions of ours, Touch for FCIs/FGs and Snow for precedence. A performance comparison of Snow-Touch to its closest competitor, Charm-L, indicates that in the specific case of dense data, the modularity overhead is offset by the speed gain of the new task order. To demonstrate our method's usefulness, we report first results of a genome data analysis application.