What obstacles prevent three-valued logic from being used as a modal logic? I am familiar with many of the surveys of many valued logic referenced in the SEP article on many valued logic, such as Ackermann, Rescher, Rosser and Turquette, Bolc and Borowic, and Malinowski. It is asserted in the article that "Many-valued logic as a separate subject was created by the Polish logician and philosopher Łukasiewicz (1920), and developed first in Poland. His first intention was to use a third, additional truth value for “possible”, and to model in this way the modalities “it is necessary that” and “it is possible that”. This intended application to modal logic did not materialize. " My question is, why didn't it?
Edited: to move summarized known objections to an answer.

I found a reference to a paper that proves that it is impossible (haven't seen the article myself) Dugundji, James. Note on a Property of Matrices for Lewis and Langford's Calculi of Propositions. Journal of Symbolic Logic 5 (1940), no. 4, 150--151. jstor, doi: 10.2307/2268175
From "many valued logic" by Reshner (1969). (Gregg Revivals page 192)  "There exist no finitely many valued logic that is characteristic of any of the Lewis systems S1 to S5 , because any finitly many-valued logic will contain tautologies that are not theorems of S5 (and fortiory not of S1 to S4 either)
