I used to have a big problem with this. My family culture values slow, serial communication, so "cooperative overlapping" of the sort practiced at my workplace came across to me as rudeness. That meant my frustration at not being heard was amplified by negative connotations about why I was getting steamrollered during meetings.
One thing that helped me was to understand the motivations of those involved. It's easy to think somebody is rude, or showing off, but fortunately I started from a place of deep respect for the capabilities of everyone in my group, and eventually a great affection for them. I saw that we had a few individuals who, if they weren't interrupting, it meant they weren't interested. After I realized this, I started to prize the guy practically jumping out of his chair to take over what I was saying, because it meant he was engaged and excited by it.
Nevertheless, I did often think about the effect on people who might be less self-confident than me, or quieter (we had a lot of students passing through in those days). In the end, if I needed to be heard, I could raise my own voice just as effectively as anybody else in the group -- but not everybody can do that.
It came to a head one group meeting, when a foreign researcher came to present some results. His presentation effectively ended after a few slides, because it got derailed by the back-and-forth of the "audience". I was really steaming and embarrassed.
He agreed to come back the following week, so I sent round an e-mail saying we had all better be on good behavior. I told the group I would bring three notebooks -- one green, one yellow, and one red. The meeting would start with the green one on top of the stack, and if I got annoyed, I would move the yellow one to the top. If the red one came to the top, I would -- well, I don't remember what I threatened, but it couldn't have been very scary, since I had no power.
In the event, the green notebook stayed on top. Not only was the group on strictly respectful behavior for the presenter, but I think it got better generally for a long time afterwards. I think seeing how that behavior affected an outsider gave everybody a little pause, and made us see ourselves better. But again, I think the details of this anecdote show what a great group of people these were. As a junior team member, I felt able to express and act on my disappointment, and everybody listened and tried to accommodate me.