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Based on e(+) e(-) annihilation data collected with the BESIII detector at the BEPCII collider, searches for the e(+)e(-) -> Sigma(c)Sigma(c) (Sigma(+)(c)Sigma(-)(c), Sigma(0)(c)Sigma(0)(c), and Sigma(++)(c)Sigma(--)(c)) processes, as well as for the process e(+)e(-) -> Lambda(+)(c)Sigma(-)(c), are conducted for the first time at root s = 4.750, 4.781, 4.843, 4.918, and 4.951 GeV. As no signals are observed for all the above channels, the upper limits on their Born cross sections at the 90% confidence level are reported. The obtained upper limits of cross sections for e(+)e(-) -> Sigma(c)Sigma(c) are more than 2 orders of magnitude smaller than those for e(+)e(-) -> Lambda(+)(c)Lambda(-)(c) near the threshold. In contrast, such suppression is absent in hyperon pair production (e(+)e(-) -> Lambda Lambda and Sigma Sigma), suggesting distinct underlying dynamics in charmed baryon production.