In my answer to your previous question, I laid out two of the most common types of social stratification. These were stratification on the basis of wealth and stratification on the basis of birth. However, there are other types of stratification that can exist along with or independent of these other types.
For example, there can be stratification based on race. There can be societies where people of one race or ethnic group are higher or lower than others based simply on that attribute. A related way of organizing a hierarchy is seen in societies like India and, to some extent, Japan which have hierarchies based on caste. There are places where the stratification is based on religion with one religion being preferred to others. These are the most common ways of dividing societies into hierarchical structures.