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No, you don't get notifications when someone comments on a post you've also commented on (but don't own). If such a feature is going to be implemented, it will be done by the Stack Overflow team. If this is important to you, you should vote up this feature-request on meta.SO. The request is currently [status-deferred], so for now you'll have to track down your most recent comments (click the "recent" tab in your user profile) and just check if somebody has replied to them.
I'm actually not sure what to think about this feature. I definitely do want to know when somebody responds to my comments, the list of comments can sometimes get long, and a new one probably isn't a response to me.
This seems to have been implemented in SO, so it should be merged into SE soon?, according to Anton's answer here.
Anyway, this is still a feature that I would really like to see, so please vote on this on meta.SE. Perhaps its incorporation into SE/MO is inevitable, but maybe extra votes will draw more attention to this / expedite the process / make sure it's more prioritized.
You know what would be nice? A list of all comments you've made sorted by date.
At least for recent comments, pages like http://mathoverflow.net/users/3?tab=recent#sort-top do the trick. I'm not sure if there's an optional argument to that URL that shows more.
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