Glad I said maximum in my first post.
Now I wonder how many theoretical reflections one private key may have.
Some sequences of bits are not on the secp256k1 curve. Some are reflections of the same point and collapse into others. So there are actually less private keys.
Since Satoshi chose this curve, a lot of research has happened in ECC. Bernstein worked out various properties that make a curve "safe", essentially means it is hard for developers to misuse the curve. secp256k1 is not a "safe" curve. https://safecurves.cr.yp.to/
Discussion
I've assumed it's just 1. But I dunno for sure. If it's just 1, and some have 0, we still have more than half as many private keys. It's still tremendously huge.