Accompaniment: Joint Participation In The Process

they	fought	hard	against the Britons
Actor	Process: material	Manner	Accompaniment

Cf they fought hard with the Britons; they and the Britons fought hard.

Halliday & Matthiessen (2014: 324):

Accompaniment is a form of joint participation in the process and represents the meanings ‘and’, ‘or’, ‘not’ as circumstantials

See also here.

cf.

they	fought	the Britons	hard
Actor	Process: material	Goal	Manner

(the Britons are being acted upon, and so: Goal, not Scope.)

cf.

they	fought	the battle	hard
Actor	Process: material	Scope	Manner