Is it possible to create "non overlapping" RNGs? For example, let's say I want two cryptographically strong RNGs (R1 and R2).
And I want them to have the following property:
R1 (resp. R2) will never generate the same random number twice.
R1 (resp. R2) will never generate a random number that R2 (resp. R1) can generate.

Is it possible for three RNGs, 4, N ?

Unlike other questions already on the site, I don't need the generated RNGs to be tracked back to their generator.
Take a block cipher with a random key and for one generator encrypt the even numbers then with the other generator encrypt the odd numbers.  Your output blocks will be pseudo-random and distinct.  For more than two generators just partition the inputs accordingly.