After going through a lot of time on this, I finally got the answer. We can nest select within expand using ; as a separator, something like
odata/Products(8)?$expand=choices($select=col1,col2;$expand=item($select=name))
This is documented in the OData v4 $expand documentation. The documentation also lists other useful examples such as
Categories?$expand=Products($filter=DiscontinuedDate eq null)
Categories?$expand=Products/$count($search=blue)