According to simulations by Canup and Ida (2014) the Earth came very close to hosting two smaller Moon’s (right) rather than the large single Moon we ended up with (left).
This fascinating ‘what if’ modelling is based on the giant impact hypothesis. A faster rate of rotation of the post impact disk is the main requirement for a two Moon system to take hold.
Of course multiple moon system are very common. Saturn for example has an abundance of them, with the most recent count totalling 82 orbiting bodies.