This technique also requires some actual authority. It may well be that the other person is interrupting intentionally and asserting (with authority) that your intended message will not be given any more time and attention and the meeting/discussion will proceed without it - which sometimes needs to be done; I've seen more than one such case happening in certain (non-internal) debates because it really needed to be done.
You can escalate and re-assert that your point is valid, but that's just escalation that can go both ways, it can result in your message being heard and it can also result in you being physically removed from the discussion; so if you choose to escalate, then you need to be certain about who'll "win" the escalation. If it's an internal team meeting and the 'interrupter' is your peer, then it's one context; if it's a customer-vendor meeting and the 'interrupter' is your boss, then that's a quite different context, and you'd better stop making that point as soon as you get a hint that it's not where he wants to direct the conversation (with the other party); your point may be valid but if making it here and now would harm the company negotiating position, then he gets to decide that your message shouldn't be told here and now.
A big aspect that's important is who's setting the topic of the discussion, and the limits of what's off-topic, disctracting or irrelevant? In an informal small discussion between peers usually that's everyone and includes you, but there are many cases where it's someone else. And in many cases that someone else should be interrupting people and ensuring that some things don't get listened to - moderating discussions is a valid need that's hard to do and often gets done less than it should, resulting in excessive ineffective long offtopic meetings.
You can escalate and re-assert that your point is valid, but that's just escalation that can go both ways, it can result in your message being heard and it can also result in you being physically removed from the discussion; so if you choose to escalate, then you need to be certain about who'll "win" the escalation. If it's an internal team meeting and the 'interrupter' is your peer, then it's one context; if it's a customer-vendor meeting and the 'interrupter' is your boss, then that's a quite different context, and you'd better stop making that point as soon as you get a hint that it's not where he wants to direct the conversation (with the other party); your point may be valid but if making it here and now would harm the company negotiating position, then he gets to decide that your message shouldn't be told here and now.
A big aspect that's important is who's setting the topic of the discussion, and the limits of what's off-topic, disctracting or irrelevant? In an informal small discussion between peers usually that's everyone and includes you, but there are many cases where it's someone else. And in many cases that someone else should be interrupting people and ensuring that some things don't get listened to - moderating discussions is a valid need that's hard to do and often gets done less than it should, resulting in excessive ineffective long offtopic meetings.