Can you go from some simple character to a more complex feature without invoking natural selection? Yes, you can. Complex features can evolve by nonadaptive means. Just think of our complex genome and read The Origins of Genome Architecture by Michael Lynch.
Want a more simple example? Read the latest post by PZ Myers: [αEP: Complexity is not usually the product of selection1.
This is an important point. You can't just assume, without question, that a complex trait must be an adaptation and must have arisen by natural selection. That applies to molecular complexes and also to complex behavior.
1. See The Evolution of Enzymes from Promiscuous Precursors for supplementary information.