Best suggestion is to use matrix.itasoftware.com to build the specific itinerary you want then search each leg independently to see how they price.
It can be even easier than that: look on Matrix for the cheapest itin between origin and destination and see if, going or returning, it's using more than one are component. If it isn't (let's say your Jacksonville-Atlanta-Seattle trip is a single component), constructing a multi-city itinerary (looking segment by segment in TTT's words) will NOT be cheaper.
Fare 1: Carrier DL UAUUA0BQ JAX to SEAPassenger type ADT, one-way fare, booking code ECovers JAX-ATL (Economy), ATL-SEA (Economy)$208.37