Camera with a non-perpendicular clipping plane

Yes, I know this probably sounds like a rather weird question for which the answer may simply be a straight no, but I still need to ask.

Using Unity, is there a way to make clipping planes work in an arbitrary orientation rather than being perpendicular to the camera?

I was a bit ahead of time with my question here, but now the question’s more acute.

In general it’s pretty easy to do clipping for the “far plane” using a shader for that, but doing the same for the near plane is a more complicated matter. Any ideas how to do that?