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
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.