I came so that they might have life and have it more abundantly.
Jesus is offering not just life, but a more abundant life. The idea that pops into my head is a glass cup with a splash of water in it. This represents the life I had before Jesus. When I accepted Him as my savior, the cup was filled. When I follow Him, my cup overflows in the abundance of life He gives me. So now the water spills over to everything around the cup.
So you see I am the cup.