If the CA is somehow able to control the communication (I think usually they don't, but if they are being run by intelligence operatives then maybe they have that capability, although they probably do not use it a lot if so (in order to reduce the chance of being detected)), they could substitute a certificate with their own keys (and then communicate with the original server using the original keys in order to obtain the information required). However, this does not apply if both sides verify by an independent method that the key is correct (and if not, would allow to detect it).

Adding multiple signatures to a certificate would be difficult because the extensions must be a part of the certificate which will be signed. (However, there are ways to do such thing as web of trust, and I had thought of ways to do this with X.509, although it does not normally do that. Another way would be an extension which is filled with null bytes when calculating the extra signatures and then being filled in with the extra signatures when calculating the normal signature.)

(Other X.509 extensions would also be helpful for various reasons, although the CAs might not allow that, due to various requirements (some of which are unnecessary).)

Another thing that helps is using X.509 client certificates for authentication in addition to server certificates. If you do this, then any MITM will not be able to authenticate (unless at least one side allows them to do so). X.509 client authentication has many other advantages as well.

In addition, it might be helpful to allow you to use those certificates to issue additional certificates (e.g. to subdomains); but, whoever verifies the certificate (usually the client, but it can also be the server in case of a client certificate) would then need to check the entire certificate chain to check the permissions allowed by the certificate.

There is also the possibility that certificate authorities will refuse to issue certificates to you for whatever reasons.