Mu's Ability to Disappear and His Bandages
This occurred to me today:
Since the Juubi's difficulty to sense is based off its Sage Chakra composition, perhaps shinobi could use Sage Chakra to mask their presence.
Normally this would not be attempted because for the Sage Chakra to cover the shinobi's chakra signature, it would have to be in a larger amount than the normal Yin and Yang chakras, and when a shinobi has more sage chakra than normal chakra, they end up turning into a sage animal and eventually into stone.
However, since Mu is an earth style shinobi, he can easily manipulate stone and if he became stone, he would still be able to move his body, similarly to controlling a stone clone, and with techniques like Onoki's that can lighten stone, he could still be completely mobile.
The bandages would serve to cover up any deformities, either flesh turned to stone or scars from partial transformation into an animal, and he could even have an entirely stone body and still look fairly normal.
This could explain a few things:
Replacing his normal chakras with Sage chakra would make him difficult to sense, because typically only senjutsu users can sense Sage chakra. (It is very possible that Sage chakra is composed of Yin and Yang chakra and can be decomposed or recombined as needed(ex: The juubi (composed entirely of sage chakra)being split into the bijuu(composed of normal chakras)). If not, he could just expel his normal chakras and absorb sage chakra which can be used for normal ninjutsu.)
Having a body of stone (besides being a reason to cover himself with bandages) would provide a simple explanation for his mitosis/body splitting technique in that he can split his rock into two and add normal rock to return him to his normal size. Since his chakra is probably only in the rock from his body, each of the two new bodies would have only half as much chakra.
Sorry if this is actually ridiculous but I felt like sharing it