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 "Secret Sharing" algorithms, most notably Shamir's Secret Sharing algorithm (thanks @heinrich5991), where the secret is split up into N pieces and given to different people for safe-keeping. To reconstruct the secret, all N pieces (or in some variants, only k of the pieces) need to be brought together. The attacker gains no information unless they have all the pieces.
These are stillAlthough used in the realm of "alternative crypto" andmany applications, I don't think any arebelieve it is available in standard crypto libraries like openssl or CAPI. You can undoubtedly findThere are many robust open source implementations -- see this question, but you'll need to do some homework to decide if you trust the implementation to not be back-doored, and some dev work to integrate it into your solution.
There is also the related concept of "Multi-party encryption"; where you encrypt the secret with multiple people's public 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 using only the RSA implementation you already have 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) )
