In response to external stimuli, naïve B cells proliferate and take on a range of fates important for immunity. How their fate is determined is a topic of much recent research, with candidates including asymmetric cell division, lineage priming, stochastic assignment, and microenvironment instruction. Here we manipulate the generation of plasmablasts from B lymphocytes in vitro by varying CD40 stimulation strength to determine its influence on potential sources of fate control. Using long-term live cell imaging, we directly measure times to differentiate, divide, and die of hundreds of pairs of sibling cells. These data reveal that while the allocation of fates is significantly altered by signal strength, the proportion of siblings identified with asymmetric fates is unchanged. In contrast, we find that plasmablast generation is enhanced by slowing times to divide, which is consistent with a hypothesis of competing timed stochastic fate outcomes. We conclude that this mechanistically simple source of alternative fate regulation is important, and that useful quantitative models of signal integration can be developed based on its principles.