You can define a notion of logical consequence that isn't preservation of truth and is therefore applicable to sentences that have no truth-values. For example, define a state as some sort of thing, define what it means for a sentence to be accepted in a state, and then define consequence as preservation of acceptance. But you still can't identify acceptance with truth because you'll have a separate notion of the truth which, in turn, is used in the definition of acceptance. It's just that this notion of truth is only defined for some sentences of the language. (As a very simple case, say a state is a set of worlds, and a non-modal sentence φ is accepted in a state s iff φ is true in all worlds w in s.)

Mark Schröder and Seth Yalcin are two people on the philosophical side who defend modal expressivism with a semantics of that sort. On the more logico-linguistic side, there's lots of Dutch people, for example Frank Veltman and Jeroen Groenendijk.