If someone has a chiyuv to say kaddish and when someone else in the minyan started to say and they (the one with the chiyuv) forgot however in the middle (or at least once the person already began saying kaddish) may they join in where the other person is holding and say at least from that point until the end?
Although I have not seen a source for this, it stands to reason that this should not be done.
The entire first half of kaddish (the part known as chatzi kaddish), from the first words (yisgadal) to the final de’amiran be’alma, is considered to be one long sentence. Although it can be argued that because somebody else has said the kaddish from the beginning, the sentence will be complete, and there’s nothing wrong with joining in the middle, it does not seem respectful to do this.
The last sentences of kaddish are independent of the first half, but here, too, it does not seem respectful to join for this part, and it might also be distracting for the person already saying kaddish, and for the congregation.