We analyze the origin of the structures observed in the reactions e + e − → 3(π + π − ), 2(π + π − π 0 ), ωπ + π − π 0 , and e + e − → 2(π + π − )π 0 around the antiproton-proton (pp) threshold. We calculate the contribution of the two-step process e + e − →N N → multipions to the total reaction amplitude. The amplitude for e + e − →N N is constrained from near-threshold data on the e + e − →pp cross section and the one forN N → multipions can be likewise fixed from available experimental information, for all those 5π and 6π states. The resulting amplitude for e + e − → multipions turns out to be large enough to play a role for the considered e + e − annihilation channels and, in three of the four reactions, even allows us to reproduce the data quantitatively near theN N threshold. The structures seen in the experiments emerges then as a threshold effect due to the opening of theN N channel.