There are two answers to your question.
1. No other private keys, if you mean the same public key (256 bits of X-coordinate plus one byte for parity of Y-coordinate and pubkey format). This is guaranteed by elliptic curve group structure. Each public point and corresponding coordinates are unique. It's true also for compressed pubkey.
I also learned that one key for one private key is guaranteed by the ECDSA. But do you know how to prove it?
I mean that there is a number of points in the amount of order. But why some 2 points generated by two different private keys could not be the same point?
There are two answers to your question.
2. Yes, huge amount of private keys, if you mean the same public address (160 bits, wallet address). Approximately there is must be 2^96 different private keys for each public address. This is provided by good statistical properties of SHA256 hash function, which was accurately tested by many cryptographers before this hash function was standardized, i'm sure. We must have unavoidable collisions for 256 bits space of input at rounding of SHA256 output to 160 bits. It is the reason for the creator of the puzzle to cancel problems from #161 to #255 some years ago, because if you can solve #160 by brute force means you can reveal privkey for any address in same time. It is not true for ECDLP, but ECDLP-race started only 4 month ago.
Actually this was my question. I'm with you that there are only 2^160 addresses, but almost 2^256 private keys. So there should a collision, because every private key could be converted to the address only in one posible way (if we are talking about the same format, like Legacy, Segwit, bech32)
When we have a private key and the address which was generated from the private key, so the x,y coordinates of the address are in the same group as the basis point. There also should be other private keys which lead to teh same address.
And I also very curious about the ability to sign with different private keys. Imagine that somebody found 2 (or may be more) different private keys to the same address. Is it possible to make outgoing transactions with the both keys or only with that one which was primarirly used? I guess that for Legace addresses it is possible. But for beech32 addresses only one unique private key should be used. Am i right?