Yes, you can do this, but you might not get the desired result. The reason you may not get the anticipated result has to do with round trip tickets and thru tickets (and maybe married segments). If "they" only sold one way tickets for a single segment, you could do what you chose, and all would be good. BUT, if you have a $200 RT from SEA-NYC-SEA, and decide instead to fly first class one direction, you get a $500 one way in coach and a $1200 one way in First. Obviously not what you wanted. But enough pricing philosophy.

Most complicated itineraries will need a ticket agent or a travel agent to book for you. While some highly experienced people here can sometimes do it, if you are not yet that sophisticated with booking engines, you probably aren't going to hit a home run this weekend. So go to a travel agent or call your favorite airline and tell them what you want. But what do you want?

You may choose to "do your homework" before calling. ITAsoftware.com allows you to build (but not book) a complex itinerary. Use sea:: /f bc=F|bc=J|bc=A|bc=I|bc=D (and if this makes NO sense to you, it also probably isn't right for you this weekend.

You might also look at fares and construct something yourself using ExpertFlyer (subscription). But I have found ITA much more practical for this kind of thing.

You have some jumping off points above, but if that sounds too complex, call your favorite agent and have them do the heavy lifting this time. And remember, they will have the same "fare rules" to fight as you do once you start mixing multiple fares on a single itinerary.