to continue moving

to argue or complain noisily (informal)

(with something / carry something on) to continue doing something

(with somebody) to have a sexual relationship with somebody when you should not (old-fashioned)

But I don't want to carry on like everything is fine, "Love in the dark" Adele
He was shouting and carrying on.
Carry on with your work while I'm away.
His wife found out he'd been carrying on with another woman.