Like many species, humans can perform non-verbal estimates of quantity through our innate approximate number system. However, the cognitive mechanisms that govern how we compare these estimates are not well understood. Little research has addressed how the human estimation-system evaluates multiple quantities, and fewer studies have considered the cost to cognitive workload when undertaking such a task. Here, we provide a novel application of Systems Factorial Technology (SFT; Townsend and Nozawa, 1995) to a comparative estimation task. Across a series of four experiments, we assess whether quantities i.e. non-overlapping red and blue discs, are estimated simultaneously (in parallel) or sequentially (in serial), and under what restrictions to cognitive workload. Our findings reveal that two item-sets may be estimated simultaneously through a parallel estimation system, under severe restrictions to cognitive workload capacity. These restrictions were so severe, as to make the parallel estimation of two quantities less efficient than the estimation of each quantity in succession. While the estimation of a single item-set may be colloquially considered an effortless process, our results show that the estimation of multiple item-sets is a rather demanding feat.