2...or was it 3 layers of lucid dreaming??

Ok so I dreamnt that I was dreaming. That was the first layer of my lucid dream. Not intentional, first time experiencing it, never tried to lucid dream. Then, in that first layer of dream, (it might get a little confusing from here sorry) I again fell asleep and was aware that I was dreaming (2nd layer of lucid dream). And I kept waking up and sleeping again btw the first and second layers. Is thateven possible?

I've had experiences like this before, but technically there are no "layers" in lucid dreaming like in inception, your dream scene just kept changing and you kept having false awakenings.