The coefficient of restitution characterizes a collision in one dimension by relating the initial and final speeds of the particles involved,
$$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$
In a 2D collision, the velocity can be split into components parallel and perpendicular to the "plane of collision" (the plane tangent to the two objects' surfaces at their contact point), and the equation above applies to the perpendicular components of the velocities only. One could write
$$\begin{pmatrix}v_{2f\shortparallel} - v_{1f\shortparallel} \\ v_{2f\perp} - v_{1f\perp}\end{pmatrix} = \begin{pmatrix}1 & 0 \\ 0 & -C_R\end{pmatrix}\begin{pmatrix}v_{2i\shortparallel} - v_{1i\shortparallel} \\ v_{2i\perp} - v_{1i\perp}\end{pmatrix}$$
My question is, is it useful (i.e. does it produce a more accurate description of realistic 2D collisions) to generalize that matrix? Perhaps by allowing the top left element to be unequal to 1, or allowing nonzero off-diagonal elements? Or is there some nonlinear relation that works better?
As usual, if you know of any relevant published research, references would be much appreciated.