表示继续/坚持做某事时用carry on with
比如carry on with your work继续（做）你的工作
表示保持某状态/某事物时用carry on
如carry on the good job(保持事物）继续努力
carry on doing sth(保持doing这个状态）继续做某事
另外后面没有接任何对象的话就不用with
ijust carry on as usual.
另外表示与某人相处的怎么样的时候用carry on (with sb)
how do you carry on with Jim
当对象在carry on后时加with
当双方都在carry on 前时用carry on除非carry on后面还有each other之类的成分
how do you (two) carry on (with each other)