Works in many ways. Can even be an WXYZ axis.
Product is one discreet thing.
Design is another discreet thing.
Engineering is too.
Manager is a thing too.
Product Design is a thing.
Product Engineering is a thing.
Design Engineering is a thing.
Product Management is a thing.
Engineering Management, and
Design Management too.
And each have their own depth and levels of knowledge. MANY various things overlap in each one and are shared.