Suppose we defined an honest agent as one who intends to focus on stating truths, with liars as those who intend to focus on stating falsehoods. But if there are other relations an agent can bear towards honesty, we end up with a broader possible moral scheme for the attendant principle-of-virtue (e.g. in a 3VL system, an agent who focuses on the post-bivalent value is not honest and is not a liar, but when {3} there is like Łukasiewicz' "possible" in one of his logical programs, then there is another aretaic status, besides "honest" and "a liar," for those who (weird as this might be) focus on stating sentences of type {3}).
Reciprocally, can we derive a justified system of 3VL (or more) by reflection from the deontic relations as initial terms of definition in this context? I.e., if we generically refer to honesty as a positive deontic state modulo "the truth in general" and lying as negative, then we project that there is a neutral truth-theoretic, and deontic, state, and this becomes a third truth-value when "reified" in physical action. This would require, it seems, that we then have a quasi-formal logic of action in place, i.e. a propositional logic with an action operator (or network of operators under the action-theoretic scheme), where the a priori question of how many truth-values to assign to the logic is decided by the logic's intended explanatory purpose (to contribute to the structural explanation of action/an explanation of the structure of action), then ramifying as every deontic relation agents can bear, on this general level, to various propositions and their patterns.
ADDENDUM: I've never considered before the option of a multiset-theoretic problem in the theory of truth-values, but there seems like there could be one (or, I get this intuition from reading the SEP entry on many-valued logic, and remembering their other entry on premise-repetition questions in substructural logic). In other words, what if we accepted something like Frege's "truth object" (as opposed to a "truth predicate") except we also accepted that there could be numerically distinct "copies" of any pure truth object? So the multiset of truth-values might be more like {T, T, T, T, ... F, F, F, F}. Now, where deontic valuations are grounded in an appeal to some non-fungible cardinal moral value of sets of agents (a common enough doctrine), this no-conflation thesis (to put it in Rawls' terms) might be read as a DVL, if you will, and then we would have the question of DMVL (where M ranges also over the types of truth-values, not only their overall multiplicity in the truth-value multiset), i.e. every agent would correspond to at least one specific truth object (whether the uniquenesses of agents would be paired with an exactly different truth object in each case, or whether there would be shared values up to universally sharable ones, I am not in a position to say, here; I only know enough about the theme to play the melody of these concepts out to this point in the question, the point of wherever we could have spelled out a sufficiently initial way how deontic functions would generate something like 3+VL in the first place (so that the greater ramifications are another story for another time)).