This will probably vary from field to field, but I've seen instances of publishing different analyses in different papers. One rich data set can yield many different analyses which may be largely unconnected with each other.
By way of example, a single longitudinal study of depression may collect data on a number of fronts; information about the participants (gender, age, location, etc), their depressive episodes, family history, genomics, neuroimaging, etc. Each of these can result in a different set of analyses, many of which would be of interest to completely different fields. A neuroscientist interested in activity patterns in the brain would not necessarily be interested in a study examining instances of suicide in high-SES vs. low-SES populations.
By thinking carefully about study design before collecting data, you can position yourself to examine questions in many different fields, leading to numerous publications.
As a final point, I'll just briefly mention that cross-disciplinary collaboration is a wonderful thing, and is very relevant to this discussion.