Well, in manga chapter 486 he says "I need to be ready for war... This is a good chance to take out the rinnegan". So he must have atleast one rinnegan, he needed it to read the information left behind by the sage of the six paths. The Sharingan could not read it but understand some parts or words of it...
So it might be that Madara can change the eye under the mask after his own likeing. If he needs the rinnegan he uses it etc etc.