Actually yes, there was a three side battle (four, if you can humans) described in the "Devourer" novel published in 2014:
Anrakyr the Traveller, Necron overlord arrives at the awakening Tomb World. He quickly manages to squash human resistance, but when he is about to reach the entrance to the Tomb, his forces are attacked by Tyranids. Unknowing to him, the Tomb has been infected by the Flyer virus, turning the freshly awakening Necrons into insane Flayed Ones.
While Tyranids have no need to attack Necron forces, they do it anyway as the Hive Mind finds their presence as a potential threat. Battle ends with
Necron forces withdrawing, seeing no reason to fight for a fallen Tomb World, but Anrakyr saves one Blood Angel Space Marine in hope that he will let him forge some sort of alliance with the chapter.
Also, from the wiki:
902.M41 The Harvest of Ka’mais – Possibly the first encounter between the Tau Empire and the Necrons, a dozen Hive Ships of Hive Fleet Gorgon assaulting the Tau colony of Ka’mais are destroyed as a fleet of Necron ships unexpectedly emerges from Ka’mais’ dead moon. Once the Tyranids are destroyed, Anrakyr lands upon the planet and is greeted with great celebration by the local Tau. Uncaring of this, Anrakyr orders the Harvest of Ka’mais, where most, if not all, of the Tau populace are killed or captured.