Just splitting the file up will not have the desired effect (as @A.Hersean explains in their answer).

I think what you're looking for is "Multi-party encryption"; where the secret is encrypted by multiple people's private keys, and then all of them need to participate in decrypting it. Here's a SO tread about it:

[Encryption and decryption involving 3 parties][1]

You can do a poor-man's version of this by chaining RSA encryption:

    RSA(key1, RSA(key2, RSA(key3, secret) ) )

If you want 3 people to encrypt, but only 2 of them need to be present to decrypt, then you can store 3 versions of the ciphertext:

    RSA(key1, RSA(key2, secret) )
    RSA(key2, RSA(key3, secret) )
    RSA(key1, RSA(key3, secret) )

There are fancier version of multi-party encryption, but they are still in the realm of "mathematical research" and I don't think any are available in standard tools like openssl.

  [1]: https://stackoverflow.com/questions/14010703/encryption-and-decryption-involving-3-parties