Can we change the hair thickness of the render? Instead of making loads of hair to add density, a cheaper option might be ot have thicker strands of hairs. Also there may be other scenarios where you want very thick hair, e.g. noodles or tentacles.
I think, you can change a single hair a bit. But it is still the behaviour of the hair to be thin, long, short, curly, etc.
Because you are working with particles, it’s possible to connect a particle to other mesh objects. And with that, manipulation of the mesh.
On Youtube there is a Blender walk through on making a rope. Under control of gravity and wind. You can us the same principle for noodles or tentacles.
As Michael explains, there are more ways to to things in Blender. And some times it’s not the most obvious ones.
With my rabbit in particular, I found that thicker hair looked more rabbit-like. However, my rabbit was a wild rabbit and they tend to have more wirey, straight hair than your domestic-bred rabbits or rabbits bred for their fluffy fur. So depending on your rabbit breed, it might work in your favour in terms of appearance to increase hair thickness.
Although, looking back on my rabbit now, there are quite a few things I would change about the fur now (such as increasing randomness quite a bit).