Coriolanus describing the people as many-headed brings together a number of interesting aspects.
First, the play contains many animal metaphors, especially because political opponents are described as beasts.
For example, Menenius talks of "Rome and her rats" in Act I, scene 1 and
calls the plebeians "beastly" in Act 2, scene 1.
Other animal references include the following:
- the bear, e.g. "As children from a bear, the Volsces shunning him" (Volumnia in Act 1, scene 3), and "He's a lamb indeed, that baes like a bear" (referring to Coriolanus, in Act 2, scene 1),
- the dog, e.g. "he's a very dog to the commonalty" (referring to Coriolanus, Act 1, scene 1),
- the dragon, e.g. in Act 4, scene 1,
- the osprey, e.g. in Act 4, scene 7,
- the tiger, e.g. "in him than there is milk in a male tiger" (Act 5, scene 4),
- the eagle, e.g. "like an eagle in a dove-cote" (Act 6, scene 6).
Not all of these animal metaphors and comparisons are negative, but if when they aren't they create distance between, on the one hand, the person being described and, on the other hand, humans generally and Romans in particular.
Second, the scene that contains the first reference to the "many-headed multitude" is Act 2, scene 3, also represents the beginning "the beginning of the great central section of the play, dealing with the clash between Coriolanus and the people" (G. R. Hibbard's edition of Coriolanus (The New Penguin Shakespeare, Penguin, 1967), page 216). If you look at the animal metaphors and comparisons used throughout the play, you will see that they are used by both sides.
Finally, there is the more genral aspect of Shakespeare's views on citizens as individuals versus citizens as members of a crowd. When citizens become members of a crowd, they lose their indviduality, their good humour and their common sense. The crowd can have an urge to destroy, so comparisons with a monster suggest themselves. For earlier examples of crowd scenes, see Act 4, scene 1 in the Second Part of Henry VI (which contains the infamous line "The first thing we do, let's kill all the lawyers.") and the crowd scenes in Julius Caesar, e.g. Act 3, scene 2.
The Hydra metaphor nicely combines these aspects of the play: if you cut off one of the Hydra's heads, it regrows two heads; when transferring this metaphor to a crowd, you risk making it more destructive by using violence against it.
