We show that free electrons can efficiently excite plasmons in doped graphene with probabilities of order one per electron. More precisely, we predict multiple excitations of a single confined plasmon mode in graphene nanostructures. These unprecedentedly large electron-plasmon couplings are explained using a simple scaling law and further investigated through a general quantum description of the electron-plasmon interaction. From a fundamental viewpoint, multiple plasmon excitations by a single electron provides a unique tool for exploring the bosonic quantum nature of these collective modes. Our study does not only open a viable path towards multiple excitation of a single plasmon mode by single electrons, but it also reveals graphene nanostructures as ideal systems for producing, detecting, and manipulating plasmons using electron probes.