Double box composite seal assembly for gas turbine engine

A seal assembly for a gas turbine engine according to an example of the present disclosure includes, among other things, a seal that has a main body extending circumferentially between opposed mate faces. The main body has a sealing portion and an engagement portion extending outwardly from sealing portion along at least one of the mate faces. The main body includes one or more braided core plies having a first fiber construction and arranged to establish an internal cavity. An overwrap having one or more braided overwrap plies follows a perimeter of the one or more braided core plies to establish the engagement portion and the sealing portion. The one or more braided overwrap plies have a second fiber construction differing from the first fiber construction. A method of fabricating a seal for a gas turbine engine is also disclosed.