Could consciousness exist outside the brain?

Probably not in the ordinary scientific sense. The strongest evidence says consciousness depends on brain activity: when the brain is damaged, altered by drugs, or stimulated, conscious experience changes too.

That said, there are serious philosophical views that leave room for a broader answer:

• Extended mind / embodied cognition: consciousness may depend on brain, body, and environment together.
• Panpsychism: consciousness is a basic feature of reality, with the brain organizing it.
• Dualism / idealism: mind is not fully reducible to the brain, so consciousness could exist independently of it.

Bottom line: neuroscience strongly links consciousness to the brain, but philosophy has not closed the question completely.