This might be too broad of a question, but it's easy to think of properties that have multiple superproperties.
Logical motivation
After all, that p is a subproperty of q just means that "x p y" implies "x q y". So all you need is some kind of relationship that simultaneously implies two different kinds of relationships:
hasSon ⊑ hasMaleRelative, hasDescendant
This makes sense, since having a son X implies having X as a male relative, and having X as a descendant, but it's not the case that either
hasMaleRelative ⊑ hasDescendant
or
hasDescendant ⊑ hasMaleRelative
That might not be a particularly motivating example, but it's simple and clear. Any time you a single property implies at least two others, you've got a property with multiple super properties.
The trivial case of multiple subproperties
Note also that because subPropertyOf is transitive, as soon as you have a multi-level hierarchy, you have multiple super properties. E.g.,
p
|
+- q
|
+- r
r has both q and p as super-properties.
Interoperability and Ontology Matching
One important reason for declaring multiple superproperties of a property is in matching different ontologies. For instance, if you're defining an ontology where text can be associated with some resource, you might want to relate your ontology with both the RDFS vocabulary and with Dublin Core. As a result, you might end up with
ex:myNote rdfs:subPropertyOf rdfs:comment, dc:description