How to require two PRIVATE keyholders to decrypt a document? Consider 3 entities A,B and C. I want A to be able to encrypt a document that can be decrypted only when keys of both B and C are combined. This question talks about a similar problem, but it uses AES. 

In my usecase, I don't want the keys to be shared across the entities. There is one solution that was coming to my mind:
A encrypts the document (with RSA) first using public key of B and then public key of C. Then the document is decrypted using private key of C and then private key of B. 

Is this approach feasible? Is there a better way?  

Note: I tried doing this but got this error when I was doing encryption for the 2nd time: Data must not be longer than 117 bytes.
Yes, you can use a symmetric secret sharing scheme, where the parts required for secret sharing are encrypted with the keys of B and C. Once B and C decrypt the parts they can combine their parts to create a symmetric data key, which is the key that is used to encrypt the document.

The very simplest way of sharing a key between two parties is to create a random data key and encrypt the document. Then create a random byte array with the same size as the data key, call it the key part of B. XOR this key part with the data key; the result is key part of C.

Now simply encrypt the key parts of the respective parties with their public keys. Now they can only access it using their private keys. For sharing, they can decrypt their part and send their key part to the other party, if required encrypted with the other parties public key. That way the final party that gets the ciphertext and both key parts encrypted with their public key. They can decrypt, combine the key parts using XOR, giving the data key. Finally they can decipher the ciphertext.

This will also solve the issue with the size of the plaintext message. RSA is limited to a certain amount of data, so in case of a 1024 bit key, you only get 117 bytes of plaintext message. However, if you use AES/GCM and RSA/OAEP in the secret sharing scheme above, then you can encrypt a message of any size with the symmetric cipher.

Note that 1024 keys are not considered all that secure anymore; you should use a key size of 3072 bits or higher. PKCS#1 v1.5 padding, that you are using, is also considered less secure nowadays due to the Bleichenbacher attacks on it.