If you're flying KLM from Rome to Amsterdam, and you're flying in Coach, I believe KLM's official policy is, you're only allowed 1 carry-on unless you're SkyTeam Elite Plus. Then you can have a second carry-on. I've seen them enforce this a few times. They walk around the gate seating area. The gate agent once told me about it, and then she saw my boarding pass said SkyTeam Elite Plus on it. . . . . Or, maybe it's just SkyPriority.