Basically I want to render everything close by, without a limit, as if the near plane is at 0 distance from the camera.
I understand this could give problems for the z-buffer, but for all I care the area ibetween the camera and the near plane can be rendered without reading and writing the z-buffer.
So is there any way to do this?
No that’s not possible for perspective cameras. A camera is infinitely small at it’s origin. The 4 “rays” of the perspective projection meet at the origin. Each of these rays go through one of your screen corners. It’s actually the space between your monitor and the virtual eye position (which is always behind the monitor). Also like you’ve mentioned when you use a very small nearplane the z-buffer accuracy is getting really bad.
An ortographic camera can have a negative nearplane since the “4 projection rays” are parallel.