Is there a way to modify this elliptic curve diffie Hellman equation like this?

Let s denote `e()` a bilinear elliptic curve pairing. Let s say I have `e(-A,B)==e(C,D)` or `e(A,B)*e(C,D)==1` where *C* and *A* are in G1 and *B* and *D* in G2. Without knowing the discrete logarithms between the points, I can alter the equation by doing something like `e(A,B+n×D)*e(C+n×A,D)==1` where `n` is a non 0 integer used as a scalar and the equation still hold.

Now, if I want to add an unrelated point *V* to *C* (I mean doing `e(C+V,D)`), is it possible to update *A* and *B* and the updated *C* without changing *D* and without computing discrete logarithms so the equation still hold?