This expanded conference paper reports the results of a psychophysiological research study on shared intentionality conducted in 24 online experiments with 405 subjects (208 recipients and 197 contributor-confederates). In this research, we created a bioengineering system for assessing shared intentionality in human groups by modeling mother-neonate dyad properties in subjects during solving unintelligible multiple-choice puzzles. In this model, only the mother (contributor-confederate) knows the correct stimulus and shares this knowledge with the neonate (participant-recipient). The bioengineering system induced interpersonal dynamics in the subjects by stimulating their interactional synchrony, emotional contagion and neuronal coherence. The system collected data by confronting recipients' performance in "primed" and "unprimed" conditions of confederates. These informed contributors knew correct responses only in the "primed" condition and confidently responded on "primed" items. Specifically, in 13 online experiments in mother-child dyads, evidence showed a recipients' performance increase of 48-394%, P-value < 0.001 (62 recipients and 54 confederates) in the “primed” condition of confederates; and in 7 experiments in primary group adults, it showed a performance increase of 143-300%, P-value < 0.002. In experiments in the secondary group, evidence showed a recipients' performance increase only with the UL3 items (a translation of an unfamiliar language, 20 recipients from 41 subjects in experiment No.12). In 3 experiments in 207 secondary group subjects, non-semantic tasks–SL3 (synthetic language) and US3 (two-color unintelligible symbols)–did not stimulate the effect. We also analyzed data confronting the outcome of recipients' performance in the "primed" condition and random value (possible recipients' responses by chance). Comparing the outcomes of these two data-collecting methods and the sample size of the experiments allow for discussing the research method's validity and reliability. The article also shows four factors' domains that contribute to shared intentionality magnitude.