Data-gathering or convergecast problems have traditionally been studied in two combinations of settings: one-shot scheduling of data items with no aggregation, and periodic scheduling of data items with full aggregation meaning that any number of unit-size data items can, if available, be aggregated into a single (unit-size) data item (e.g., by summing or averaging values). In this paper, we extend beyond these problem settings in two ways. First, we study a) one-shot throughput maximization in settings with aggregation and b) periodic scheduling in settings without aggregation. Second, we generalize the notion of aggregatability in both one-shot and periodic scheduling beyond the binary choice of either all sets of items being aggregatable or none being so. Modeling the presence of multiple semantic data types (e.g., target counts to be summed and temperature readings to be averaged), we partition data items into classes, whereby items are aggregatable if they belong to the same class, in both periodic and non-periodic settings. For these two problems we provide guaranteed approximations and heuristics, for a variety of general and special cases. We then evaluate the algorithms in a systematic simulation study, both under the conditions in which our provable guarantees apply and in more general settings, where we find the algorithms continue to perform well on typical problem inputs.