We show that free electrons can efficiently excite plasmons in doped graphene with probabilities in the order of 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 provide a unique platform for exploring the bosonic quantum nature of these collective modes. Not only does our study open a viable path toward multiple excitation of a single plasmon mode by a single electron, but it also reveals electron probes as ideal tools for producing, detecting, and manipulating plasmons in graphene nanostructures.