Communication is an indispensable part of the public life of human beings as social creatures. Social interaction among people happens mostly when mediated by language. It is generally believed that for smooth communication and mutual understanding during a natural social interaction, individuals as interactants follow the Cooperative Principle (CP) and its four conversational maxims. In recent two decades, with the advent of Social Networking Services (SNSs), a virtual dimension has been added to daily face-to-face interactions, thus opening a new line of inquiry for researchers to explore whether the same principle or maxims govern digitally mediated communications in such online social interactions. Thus, this study accounted for violating Gricean’s four maxims of conversational implicatures on Instagram. It investigated how much quantity, quality, relevance, and manner maxims were observed in the native vs. non-native English users’ written posts on social networks and to what extent the posters violated them. Attention was paid to the cases of violations, particularly the quantity maxim. A non-experimental, descriptive design was employed to analyze 240 data collected from 40 English natives and non-natives. The posts were collected for 4 months in 2022 and analyzed using descriptive statistics in frequency and percentage, and then Chi-square tests were run. The findings revealed that cultural differences and participants’ gender were influential variables. Both groups favored violating the quantity maxim and exchanged many brief messages. Both groups had near percentages for quality and manner violations, but non-native Iranian students violated the relation maxim more than natives. The findings showed that cultural competence was central to pragmatic knowledge, which could be attained through social interactions. It was suggested that second-language pragmatic competence could be discussed in terms of intercultural and cross-cultural competence.