Effect of redundant training data in HMM-based speech recognizer/synthesizer? How are redundant training data handled during the training stage?

For example, assume we have one observation for phone $\theta$ in the training set.

Then the training (for a monophone) is done with: 

$$\lambda_{max}^\theta = \text{arg} \max_\lambda p(\bf{O}|\lambda) $$

where $\bf{O}$ is the observation sequence and $\lambda$ is the HMM model.

This is straightforward when only a single observation is available from the training set. But what happens when there are multiple observations for phone $\theta$ in the training set? How is $\bf{O}$ adjusted?
I guess you confuse GMM and HMM trainings. Although in both cases EM algorithm is employed, Baum-Welch is used for HMM training.