Plutarch adapted
Shakespeare admired Sir Thomas North's translation of Plutarch's Lives--so much that at times he came close to simply transcribing North's excellent prose.
He did not always follow North, however. He changed the chronology of events or condensed them to make them more stageable.
In some cases it is not clear whether Shakespeare made changes for dramatic or ideological reasons: the crowd of plebians in Shakespeare is more fickle than is reported in his sources--a change which makes them more threatening (and thus more dramatic), but which also fits into the conservative attitude of authority to the sometimes restive Elizabethan populace.