from what I have read,

a private key is a 256 bit binary number.

private key ----------elliptic curve multiplication-----> public key

public key -----------sha256 + ripemd160 -----------> public key hash

public key hash -------base58 check encoding------> bitcoin address

now according to the above,

2²⁵⁶ private keys are possible
since elliptic curve multiplication produces a unique public key from each private key, an equal number of corresponding public keys are also possible. But, since the public key goes through RIPEMD160, the public key hash has only 20 bytes or 160 bits. Hence only 2¹⁶⁰ bitcoin addresses are possible. Does this mean that each bitcoin address may be associated with more than one private key? Since, if each of 2²⁵⁶ public keys produce only 2¹⁶⁰ hashes this means more than one public key produces the same public key hash.

I would appreciate if an expert could clarify this matter ?