Grouping vehicles into platoons promises to improve road capacity, driver safety, and fuel consumption. However, when platoons have to allow for cross traffic maneuvers, the ability to control single large platoons is not sufficient, and chaining smaller platoons becomes necessary. To this aim we define PLATO, an edge-assisted multi-platoon control architecture and, by delving into the dichotomy of unity and plurality of platooning, we analyze costs and benefits of multi-platooning. We investigate on the feasibility and formulate the utility of multi-platoons by analyzing the underlying edge computing and broadband cellular connectivity requirements. Using a detailed simulator, we show that, in realistic environments, multi-platoons can be effectively controlled with PLATO, as long as the latency between individual platoon managers and the multi-platoon manager is kept below a few tens of milliseconds. Surprisingly, the latency between vehicles and managers is one order of magnitude less critical.