The allegory very specifically requires the removal and destruction of "main branches" of the tree. Translating image to history, the main event of this part of the allegory is the destruction of the established power structure of Israel. Two parts of the event are listed, the destruction of the "main branches" and the grafting in of "wild branches." These are events that can be correlated to historical events, but not events which will fit precisely into the timetable of the allegory. Allegories, however, as part of a symbolic explanation need not parallel every historical event. It is sufficient that we may recognize the event, and it is not required by the literary form that all elements of the allegory fit the historical situation precisely.
The "destruction" of Israel occurs in three places that have relevance to this allegory. The first is the Assyrian destruction and the loss of the ten tribes in the 722-721 BC the second is the Babylonian destruction of 586 BC, and the third is the destruction of Jerusalem in 62 AD. The destruction of the main branches is suggestive of the first dispersal rather than the second, as the Assyrians did not only kill many but effectively "destroyed" the remainder by their permanent removal from Israel. In the
Babylonian conquest, the people were carried away, but returned, and our history is one of that very people, so they do not fit the allegory at this point. The destruction by the Romans fits as a category, but the removal in time suggests that it is not imagined by this part of the allegory.
The "grafting" of the wild branches might refer to an intermarriage with the Babylonians who might have entered Judah after the conquest, but there is no evidence of the importation of foreign populations into Jerusalem after the leadership had been removed (Gottwald, Norman K. The Hebrew Bible . Fortress Press, 1985., p. 424). Hoskisson suggests intermarriages for both the Babylonian and Assyrian destructions (Hoskisson, p. 78).
The ultimate assignment of the historical event to the grafting depends more on the nature of the allegory than of history. While intermarriage does bring in new blood, the effect of the new blood is to invigorate the root of the tree (the identification of which will be discussed after the next verse). The grafting image is therefore to suppose a positive addition to the tree, and it is hard to imagine a scenario where the intermixing of cultures with gentiles would have been considered beneficial to covenantal Israel (Hoskisson uses the cultural melding as an indication of the grafting process, see Hoskisson, p. 79).
The clearest reference for grafting is to the adoption of the gentiles into the Abrahamic covenant as described in Paul's use of the olive tree allegory. The events following this verse in the allegory suggest that this latter interpretation is the one that is being used.