How can one convert an SSL cert provided by an authority to another authority, so one can generate "valid" certs for different domains?
What you are looking for is to modify the certificate in a way that it contains the ability to be a CA, i.e. set the CA flag to true. Fortunately you cannot simply modify a certificate, because any kind of modification invalidates the signature and thus nobody will trust this certificate anymore. This is essential because otherwise everybody could just create certificates for sites they don't own and this do man in the middle attacks.
You can't do this, you will have to apply for a new certificate. There are special types of certificates that apply for multiple previously specified domains at once.