Create a custom physics joint

Is it possible to extend the physics system (2d or 3d) with my own joint? I would like to create something like the RelativeJoint2D or FixedJoint2D but have them work in different coordinate systems (non-euclidean physics for example). I have created a version that seems to almost work correctly, but I think I need to be able to hook into the velocity & position iterations to make it work correctly.

My current "constraint" code is this:

Create a custom physics joint