Uncovering the mechanisms that control size, growth, and division rates of organisms reproducing through binary division means understanding basic principles of their life cycle. Recent work has focused on how division rates are regulated in bacteria and yeast, but this question has not yet been addressed in more complex, multicellular organisms. We have, over the course of several years, assembled a unique large-scale data set on the growth and asexual reproduction of two freshwater planarian species, Dugesia japonica and Girardia tigrina, which reproduce by transverse fission and succeeding regeneration of head and tail pieces into new planarians. We show that generation-dependent memory effects in planarian reproduction need to be taken into account to accurately capture the experimental data. To achieve this, we developed a new additive model that mixes multiple size control strategies based on planarian size, growth, and time between divisions. Our model quantifies the proportions of each strategy in the mixed dynamics, revealing the ability of the two planarian species to utilize different strategies in a coordinated manner for size control. Additionally, we found that head and tail offspring of both species employ different mechanisms to monitor and trigger their reproduction cycles. Thus, we find a diversity of strategies not only between species but between heads and tails within species. Our additive model provides two advantages over existing 2D models that fit a multivariable splitting rate function to the data for size control: firstly, it can be fit to relatively small data sets and can thus be applied to systems where available data is limited. Secondly, it enables new biological insights because it explicitly shows the contributions of different size control strategies for each offspring type.