Re-encrypting a message and proving that the message has not changed Is there a method that allows for re-encryption of a message in a way that allows observers who only have access to the two cipher texts to prove that the plain text message is the same in each?

More specifically: if I have a message $m$, and I encrypt it with an asymmetric key scheme $E_1: c_1 = E_1(m)$ and then re-encrypt it with a new key pair $E_2: c_2 = E_2(m),$

is there a way for an observer (possibly using a ZKP or homomorphic encryption) who only has access to $c_1, c_2$ and the public keys of $E_1$ and $E_2$ to prove that $m$ is the same plain text used to generate $C_1$ and $C_2$?
I  think this is not compatible with semantic security (IND-CPA). If such a proof exists,  an adversary that chooses $(m_0,m_1)$ and receives $c_b=E_1(m_b)$ may compute $E_2(m_0)$ and try to prove that $m_b=m_0$. If the proof is correct, then he guesses that $b=0$, else $b=1$. But may be there exist weaker security models that allow to test the equality of two plaintexts.
Your problem seems similar to plaintext checkable encryptions.