It seems you are just looking to specify a set of bounds, not really do an
affine transformation to rotate, shift, shear, etc.
It is done in the following manner:

Summary:  Creating a custom projection with specific bounds.

Question:  How can a custom projection be created with specific bounds ?

Answer:  The syntax that should be used in the MAPINFOW.PRJ file is:

     name, projection number + 2000, projection parameters, x1, y1, x2, y2

**The bounds are expressed in units of the coordinate system as well just like
the False Eastings and Northings.

In the below example, a Transverse Mercator projection, (e.g. Australian Map
Grid using AGD66 datum) with specified bounds of (0, 5500000) (1000000, 6500000)
in meters should be written as:

"Custom projection name", 2008, 12, 7, 147, 0, 0.9996, 500000, 10000000, 0,
5500000, 1000000, 6500000

Regards,
-Bill


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