Well this is assuming the Rinnegan isnt an Uchiha-exclusive power, which is what I think as it has been heavily implied that it is a Senju + Uchiha DNA power, even if you dont believe it, bear with me at least for the sake of the theory.
This theory is to suggest there are different kinds of Rinnegan and utilities, becuase the Rinnegan unlike other abilities is not a closed power. What do I mean by closed power? Take for example a Kagebunshin, you make the seals, perform the technique and you know it is going to always spawn a clone. The known MS (bar Kakashi's) work on the same way you know there are 3 techniques and thats it, same for Byakugan. The Rinnegan appears to be the exception and while has some pre-determinated powers (paths) , you can work anything you want with it and get completely new techniques that werent there, combine them, etc.
The Uchihas
Again it is heavily implied the Rinnegan requires Senju and Uchiha DNA, it is activable via the EMS, this appear to the Uchiha version of Rinnegan I think there are different versions. The Uchihas go to their highest point, EMS then in my theory if you give then Senju DNA or some other unknown mechanism which havent been revealed the Uchiha will develop the Rinnegan, gaining not only the paths but the ability to combine their already massive techniques with Rinnegan to develop entirely new and deadly techniques for example Susanoo, they can turn off the Rinnegan and switch from EMS, Sharingan etc.
Nagato
Nagato being Senju part (Uzumaki) is a special case, you could say he is in a way the "Kakashi" of the Rinnegan as he couldnt turn it off and he only had the Rinnegan pre-determinated abilities (paths, and afinity with all the elements). This in my theory is because he didnt developed it naturally which would allow for the plethora of powers Rinnegan would allow to, had he reached the pinnacle of his Uzumaki heritage and then got Uchiha DNA or whatever mechanism is requried to activate it, he would be at the level of Madara, but he didnt it appears he simply had the Rinnegan transplanted into his eyes. We cant say Nagato was a "false Rinnegan user" in any way, like we could say of Kakashi, since he was a Senju and such suitable for said power just as Senjus and Uchihas are suitable for said powers, indeed further proof that he was a true wielder of the Rinnegan is that Madara acknowledge him as a Rikudou as evidenced by the fact that in the chapter when he gained his complete body again was called "the Rinnegan used properly".
However we can agree that his abilities arent at the level of Madara, watch as even complete Nagato took some time to cast even a Chibaku Tensei, Madara brings a meteor with zero effort and in no time. This however isnt because Nagato isnt a true wielder while Madara is, it is simply because Madara had activated his Rinnegan the natural way and had way much more ground to work with and use the Rinnegan innovation capacity, while Nagato apparently being just a mere transplant while using it properly only worked with the pre-defined abilities of Rinnegan and didnt had much ground and experience to innovate.
Senju - possibly bodily Rinnegan
Now here comes the Senju which appear to somehow be the underdogs in this situaiton, as effectively some people ask "Uchihas has MS, MS and EMS, Senju? nothing!". I dont think this is the case.
The Uchihas needs to to take out their brother's eye, it would appear as evidence by Naruto's transformation that a Senju needs to inject shitloads of chakra in their body to have the equivalent power-ups. It simply means they have different requirement for their powers and in Naruto's case this is the first time we see it, it would be logical that the more chakra you put into a Senju body the stronger it becomes. Obviously Naruto's transformation is because of the Kyuubi chakra however there are some aspects that at least for me are obviously part of his Uzumaki heritage (body of the sage) mixed with a Bijuu gave him some qualities like the immense life-force, I really doubt that for example Bee would get the same qualities as Naruto if he got Kyuubi, he would possibly simply get a chakra shroud.
So in my theory the Senju too when they reach the height of their power (whatever that may be) just as like when the Uchiha reach the height of their power if mixed with some Uchiha DNA or whatever unknown mechanism is needed to manifest Rinnegan, will too get the Rinnegan or an equivalent in their Senju form. However instead of being spiritually oriented like Madara's Rinnegan will be more bodily and physically oriented, this isnt necessarily because they cant use the spiritual qualities of the Rinnegan, after all they would have Uchiha DNA and become a Rikudou (as Madara said, having both the abilities of Uchiha and Senju) however it would be more bodily oriented simply because the development of their abilities up to that point was bodily oriented and thus would be easier to use the Rinnegan's capacity to innovate powers with their already massive background than simply starting over.
How would a Rinnegan manifest in the Senju or Uzumaki? I dont know, they could have the Rinnegan in their eyes too representing they embody both powers, even if their use will be completely different from what we saw of Nagato and Madara. However I think the manifestation will be a bodily representation of it.
So when Naruto reach the height of his power, whatever that may be if he gets to do whatever method is requried to manifest Rinnegan he will get it in a bodily form. My guess is that perhaps the swirls (that are oddly enough equal to the elder son eye) may turn while using his RM (Chakra Mode) into concentric circles, thus amping his attacks to the nth degree.
Anyway just my 2 cents, trying to tie the Senju and Uzumaki in.
This theory is to suggest there are different kinds of Rinnegan and utilities, becuase the Rinnegan unlike other abilities is not a closed power. What do I mean by closed power? Take for example a Kagebunshin, you make the seals, perform the technique and you know it is going to always spawn a clone. The known MS (bar Kakashi's) work on the same way you know there are 3 techniques and thats it, same for Byakugan. The Rinnegan appears to be the exception and while has some pre-determinated powers (paths) , you can work anything you want with it and get completely new techniques that werent there, combine them, etc.
The Uchihas
Again it is heavily implied the Rinnegan requires Senju and Uchiha DNA, it is activable via the EMS, this appear to the Uchiha version of Rinnegan I think there are different versions. The Uchihas go to their highest point, EMS then in my theory if you give then Senju DNA or some other unknown mechanism which havent been revealed the Uchiha will develop the Rinnegan, gaining not only the paths but the ability to combine their already massive techniques with Rinnegan to develop entirely new and deadly techniques for example Susanoo, they can turn off the Rinnegan and switch from EMS, Sharingan etc.
Nagato
Nagato being Senju part (Uzumaki) is a special case, you could say he is in a way the "Kakashi" of the Rinnegan as he couldnt turn it off and he only had the Rinnegan pre-determinated abilities (paths, and afinity with all the elements). This in my theory is because he didnt developed it naturally which would allow for the plethora of powers Rinnegan would allow to, had he reached the pinnacle of his Uzumaki heritage and then got Uchiha DNA or whatever mechanism is requried to activate it, he would be at the level of Madara, but he didnt it appears he simply had the Rinnegan transplanted into his eyes. We cant say Nagato was a "false Rinnegan user" in any way, like we could say of Kakashi, since he was a Senju and such suitable for said power just as Senjus and Uchihas are suitable for said powers, indeed further proof that he was a true wielder of the Rinnegan is that Madara acknowledge him as a Rikudou as evidenced by the fact that in the chapter when he gained his complete body again was called "the Rinnegan used properly".
However we can agree that his abilities arent at the level of Madara, watch as even complete Nagato took some time to cast even a Chibaku Tensei, Madara brings a meteor with zero effort and in no time. This however isnt because Nagato isnt a true wielder while Madara is, it is simply because Madara had activated his Rinnegan the natural way and had way much more ground to work with and use the Rinnegan innovation capacity, while Nagato apparently being just a mere transplant while using it properly only worked with the pre-defined abilities of Rinnegan and didnt had much ground and experience to innovate.
Senju - possibly bodily Rinnegan
Now here comes the Senju which appear to somehow be the underdogs in this situaiton, as effectively some people ask "Uchihas has MS, MS and EMS, Senju? nothing!". I dont think this is the case.
The Uchihas needs to to take out their brother's eye, it would appear as evidence by Naruto's transformation that a Senju needs to inject shitloads of chakra in their body to have the equivalent power-ups. It simply means they have different requirement for their powers and in Naruto's case this is the first time we see it, it would be logical that the more chakra you put into a Senju body the stronger it becomes. Obviously Naruto's transformation is because of the Kyuubi chakra however there are some aspects that at least for me are obviously part of his Uzumaki heritage (body of the sage) mixed with a Bijuu gave him some qualities like the immense life-force, I really doubt that for example Bee would get the same qualities as Naruto if he got Kyuubi, he would possibly simply get a chakra shroud.
So in my theory the Senju too when they reach the height of their power (whatever that may be) just as like when the Uchiha reach the height of their power if mixed with some Uchiha DNA or whatever unknown mechanism is needed to manifest Rinnegan, will too get the Rinnegan or an equivalent in their Senju form. However instead of being spiritually oriented like Madara's Rinnegan will be more bodily and physically oriented, this isnt necessarily because they cant use the spiritual qualities of the Rinnegan, after all they would have Uchiha DNA and become a Rikudou (as Madara said, having both the abilities of Uchiha and Senju) however it would be more bodily oriented simply because the development of their abilities up to that point was bodily oriented and thus would be easier to use the Rinnegan's capacity to innovate powers with their already massive background than simply starting over.
How would a Rinnegan manifest in the Senju or Uzumaki? I dont know, they could have the Rinnegan in their eyes too representing they embody both powers, even if their use will be completely different from what we saw of Nagato and Madara. However I think the manifestation will be a bodily representation of it.
So when Naruto reach the height of his power, whatever that may be if he gets to do whatever method is requried to manifest Rinnegan he will get it in a bodily form. My guess is that perhaps the swirls (that are oddly enough equal to the elder son eye) may turn while using his RM (Chakra Mode) into concentric circles, thus amping his attacks to the nth degree.
Anyway just my 2 cents, trying to tie the Senju and Uzumaki in.