The behavior of minor hysteresis loops in perpendicular anisotropy Co/Pt and Co/Pd multilayers has been investigated. Upon applying a succession of identical magnetic field cycles, we observe a very substantial cumulative growth of the minor loop area. For the Co/Pt multilayers this effect only saturates near complete magnetization reversal while the behavior is slightly more limited for Co/Pd multilayers. We also find this cumulative growth to occur even if the minor loop field cycles are made asymmetric by means of a positive bias field. The cumulative behavior persists up to a sample-dependent threshold value above which this effect disappears. In all samples, the cumulative minor loop growth is correlated with a small reduction in the maximum magnetization value in each cycle. Magneto-optical Kerr microscopy studies correlate the minor loop growth with the memory and cumulative expansion of lateral domain cycling. All experimental observations can be consistently explained as an accumulation of small nucleation domains that aid subsequent reversals and facilitate the cumulative minor loop growth.