Many independent pseudorandom graphs each with same arbitrary y for any input x
Well you're probably going to need to come up with some more detailed requirements but yes, there are ways: 

pre-populate a dictionary with however many terms in the series you require for a given seed and then at run-time simply look the nth term up. 
if you're not fussed about the seed values and/or do not require some n terms for any given seed, then find a O(1) way of generating different seeds and only use the first term in each series.  

Otherwise, you may want to stop using the built-in python functionality & devise your own (more predictable) algo. 
EDIT wrt the new infos:
Ok. so i also looked at your profile & so you are doing something (musical?) other than any new crypto thing. if that's the case, then it's unfortunately mixed blessings, because while you don't require security, you also still won't want (audible) patterns appearing. so you unfortunately probably do still need a strong prng.

One of the transformers that I want adds a random value to the input y
  coordinate depending on the the input x coordinate

It's not yet clear to me if there is actually any real requirement for y to depend upon x...

Now say that I want two different instances of the transformer that
  adds random values to y. My question is about my options for making
  this new random transformer give different values than the first one.

..because here, i'm getting the impression that all you really require is for two different instances to be different in some random way.
But, assuming you have some object containing tuple (x,y) and you really do want a transform function to randomly vary y for the same x; and you want an untransform function to quickly undo any transform operations, then why not just keep a stack of the state changes throughout the lifetime of any single instance of an object; and then in the untransform implementation, you just pop the last transformation off the stack ?
By 'graph' I mean 'function' in the mathematical sense, where you always find one unchanging y value per x value.
Python's random.Random class's seed behaves as the x-coordinate of a random graph and each new call to random.random() gives a new random graph with all new x-y mappings.
Is there a way to directly refer to random.Random's nth graph, or in other words, the nth value in a certain seed's series without calling random.random() n times?
I am making a set of classes that I call Transformers that take any (x,y) coordinates as input and output another pair of (x,y) coordinates. Each transformer has two methods: transform and untransform. One of the transformers that I want adds a random value to the input y coordinate depending on the the input x coordinate. Say that I then want this transformer to untransform(x, y), now I need to subtract the same value I added from y if x is the same. This can be done by setting the seed to the same value it had when I added to y, so acting like the x value. Now say that I want two different instances of the transformer that adds random values to y. My question is about my options for making this new random transformer give different values than the first one.