Homography of plane parallel to a plane with known homography

Question

Please refer to the following image:

homography-question.jpg

Details:

1. P1, P2, P3, and P4 are in a plane, say, Plane1.
2. P5, P6, P7, and P8 are also in a plane, say, Plane2.
3. Plane1 and Plane2 are parallel.
4. World coordinates of P1, P2, P3, and P4 are known, but P5, P6, P7 and P8 are not.
5. However, Plane2 is known to have a distance d from Plane1.
6. In the image above, the projections of Plane1 and Plane2 (in red and blue, respectively) are shown.
7. The projection plane is not parallel to Plane1 and Plane2.

Question:

With the known world coordinates of P1, P2, P3 and P4, and image coordinates of P1', P2', P3', and P4', I can reconstruct the image such that it can have its original shape using homography of Plane1 to the projection plane.

However, I am more interested in reconstructing Plane2. Is it possible to determine the homography of Plane2 to the projection plane in this situation?

Think of this problem that the world coordinates of P5, P6, P7 and P8 are difficult to measure.