I'm also not sure I totally understand the question, so correct me if I misunderstood you. Here's what I understood: you have the orbital elements of two orbits A and B, and would like to define orbit A as the new reference frame, and express the orbit B with respect to that reference frame A.
If so, yes, that's possible, and not to difficult. In effect, an orbit is simply a rotation. We can compute rotations in different ways. I prefer Modified Rodriguez Parameters, but these aren't that popular yet, so let's use Euler Parameters (also called Euler Angles).
Let me explain. Start from an Earth Inertial Frame. First, do a rotation by the Z (or third) axis of your right angle of the ascending node. Then do a rotation by the X axis (or first axis) by your inclination. Finally, do a rotation about the Z axis (again) of your true anomaly. So, in terms of Euler parameters, you've done a 3-1-3 rotation (i.e. multiply the R3, R1 and R3 matrices together computed with the correct angles to get your direct cosine matrix (DCM)).
Using DCMs, you just need to multiply both DCMs to change the reference frame, and of course multiply that with the R vector of your spacecraft.
(I highly recommend "Analytical Mechanics of Space Systems (AIAA Education Series) 2nd Edition" by Dr. Schaub and Dr. Junkins for any astrodynamics question by the way. The above computation is thoroughly explained in chapter 3.)