One source of power in every interaction is interruption. Those with power interrupt, those with less power get interrupted. In conversation, interrupting others, although not polite, can indicate power and be an effective power move, something noted by scholars in a field called conversation analysis. Men interrupt others more frequently than women, and doctors seldom listen to their patients for very long without interrupting. In each instance, patterns of conversation reinforce differences in power and status derived from other sources such as general social expectations and expert authority.
Watching the Oliver North and Donald Kennedy hearings illustrates this phenomenon. North on one occasion stops an interrogator’s anticipated interruption by holding up his finger and saying, “Let me finish.” He refuses to be interrupted and in several other instances talks over the lawyers and legislators questioning him. By contrast, at one point Donald Kennedy requests permission to continue speaking, asking, “Can I continue?” and thanks the congressman when permission is granted.
I can't stand it when people ask "can I continue?" They are trying to shame the other person out of interrupting them. Like most attempts to take the moral high ground, though, I find that it just comes off as whiny and ineffectual. It's victim behavior. Its message, at its core, is "I have been wronged, you have wronged me." But it's very difficult to make victimization work for you as a power move. I think most people look at victims and don't think "powerful" but "weak." Especially over something so small as interrupting and especially for a proceeding in which the ostensible aim is the truth, the overall effect of this type of behavior is to make the person seem overly defensive and like they are trying to hide something.
I've actually seen a lot of people be taken down in the comments section via this weakness, trying to enforce false rules of engagement on others like good sportsmanship or good grammar or however it is that they think this gentleman's game of warfare should be played. Courts use a certain degree of formality and adherence to rules, but in the court of public opinion I have found that being overly rigid in following any sort of "rules" just makes you look like you are trying and failing to play a game of smoke and mirrors. There's a reason why everyone hates lawyers.