I have to be honest. I don’t like the phrase “system”. It makes us sound like machines.

As I understand it the term system is meant similarly to ‘star system’: 

A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction.

Like a star system, systems of headmates are all independant people who ‘orbit’ one another bound by  one body and brain.

The term has been in use for quite a long time, and is generally accepted However there are those who use their own terms.