No, it doesn't reduce the number of passwords that could be used.
Generally a password is used to derive a symmetric key. It is good practice to use a Password Based Key Derivation Method (PBKDF) for that. Usually that PBKDF uses a salt and work factor (and possibly other parameters). The salt - which is included with the ciphertext - makes sure that the key always differs, even if the same password is used. Furthermore, the PBKDF is a one-way password hash, so it is also impossible to get from the key, other than to try every password. Furthermore, the key in itself is protected by the cipher used; it therefore should remain protected even if multiple plaintext / ciphertext pairs are known.
As a PBKDF is a password hash with a specific capacity as well as output size, it may be that multiple passwords hash to the same value. However, this is by chance, and finding them is next to impossible. Generally, if a dictionary attack is used then you can assume that the password is guessed correctly if the correct key is found. Having multiple ciphertext to compare against doesn't make a difference.
Note that this is about best practice symmetric encryption. If you'd use e.g. the Vigenere cipher then yes, encrypting with the same password would break the entire scheme.
Furthermore, you could e.g. encrypt a private key instead and use the corresponding public key to encrypt files. In that case you'd only need the password when decrypting files.
Finally, if the same key is used to encrypt a file then having many, many blocks of plaintext data may make a difference; some information may leak e.g. if to CBC block encrypts will generate the same ciphertext (meaning that the input block is also identical). Or when the counter used within CTR encryption is overflowing, etc. etc. However, as stated, usually you'd still use different keys, even if the same password is used. In that case the only limiting factor is the message / file size.