The words 'together with', 'along with', 'as well as' and

An easier way to understand is to see what the focus of the sentence is.
Suppose you have two main subjects say The prime minister and his secretary and they both went for a meeting.
Would you say " The Prime minister and his undersecretary went for the meeting ?
or The prime minister along with his undersecretary went for the meeting.
Obv the Second one because the priminister is the focus of the sentence it. and that is the reason we use Together with, along with because we want he focus to be on one of the subjects. The use of and accords equal importance to both of the subjects where as the use of together with and along with tells us that the first one is the main subject we are talking about. and hence singular.