Both RSA and Elgamal have homomorphic properties. So both can re-encrypt the ciphertext. Re-encryption with Elgamal works as seen here.
How does re-encryption work using RSA?
What modification / addition is needed to transform simple RSA to RSA with re-encryption?
The keys for RSA:
Public key: $e$ & $n$
Private key: $d$
Encryption: $C=M^e \bmod n$
Decryption: $M=C^d \bmod n$
I read this answer and it's very similar to what I am looking for. But I have practically a few limitations (as it is textbook RSA, and I have security flaws). I have an arbitrary length (large) plaintext. I want to encrypt it with RSA. I want to re-encrypt the ciphertext (independently and multiple times). Also I don't understand this formatted plaintexts in this question.
Is there a practical scheme / implementation available?
What changes are there needed in RSA to re-encrypt a ciphertext without compromising security?