You really have to decide what you mean by a "trilogy". It isn't really a rigorously defined form.
If it really is a sort of three act play of epic proportions, then yes, you really don't have a separate premise to work out. In your sequels, you're just doing the second and third acts of the same story. But a series of books (whether it be three or some other number) doesn't have to be a single "arc".
For examples, let's compare the grandfather of all trilogies, Lord Of The Rings, to everyone's favorite modern fantasy example, Harry Potter.
Ironically, the trilogy was written in six volumes, rather than three; it was a later publishing decision to put two 'books' per volume into three volumes. So we are actually comparing six books to six books. Or are we?
Realistically, LOTR is not three books, or six books. It does have several arcs, but they overlap each other, so you can't divide the book conveniently that way. When you get down to it, Tolkien wrote a single novel, and simply published it in more portable chunks than how Tolstoy handled the similar-sized "War and Peace."
In contrast, the chronicles of Mr. Potter are not a single novel. They really are six stories. They certainly don't stand apart from each other, but they relate to each other like The Hobbit relates to LOTR, rather than the way the volumes of LOTR relate to each other. There is an arc of sorts that ties them together, but it is secondary to the more compelling arcs told by each book.
My point is that how you go about addressing your books should depend upon which of these models they follow. These assignments are subordinate to your story, not the other way around, so use them the way that serves your novel best.
...
Regards,
Eric Fretheim
"It is perfectly okay to write garbage-- as long as you edit brilliantly." ~C.J. Cherryh
"Success is the ability to go from failure to failure without losing your enthusiasm." ~Winston Churchill
āNo, writing 50,000 words in a month is
normal. You are
not crazy. This is
not insane.ā ~Teri Brown