Is it possible to have multiple Conjugate Priors? In Bayesian probability theory, can a probability distribution have more than one conjugate prior for the same model parameters? 
I know that the Normal distribution has another Normal distribution or the Normal-Inverse-Gamma distribution has conjugate priors, depending on what the model parameters are.
If multiple priors exists, then kindly cite some. If multiple priors do not exist, what is the proof that it cannot exist?

If you have a conjugate prior density $f(\theta)$, then $h(\theta)f(\theta)/\int h(\tilde{\theta})f(\tilde{\theta})\,d\tilde{\theta}$ is another conjugate prior for any positive $h$ that is integrable wrt $f$. One therefore typically speaks of a conjugate prior rather than the conjugate prior.
