The manga shows that upon activating the Rinnegan near death, Madara then passed his eyes onto Nagato.
I understand that Nagato, being an Uzumaki, could only access the power granted by the Rinnegan and not any other Sharingan powers because he isn't an Uchiha. Edo Madara, on the other hand, is able to access all three stages of his dojutsu powers - Sharingan, EMS and Rinnegan.

So my point is....

When Tobi faces Konan and uses Izanagi, he gets rid of a replacement sharingan eye from his collection and goes to take Nagato's Rinnegan eye, implanting it in his left eye. Because Obito is implanted with Senju DNA, and is an Uchiha, not only should he have Rinnegan in his left eye, but should also have access to Madara's Sharingan as well as his Mangyeko Sharingan (note it's not eternal because they're not related).

Does this work? Or do you have to literally go through each evolutionary stage (Sharingan -> MS -> EMS -> Rinnegan) to have access to all three abilities? Discuss...