DOMES
If 4 then M is third as the only change from DOSES to DOMES was S->M and the score added one.
If 2 then S is second as the only change from DOSES to DOMES was S->M and the score dropped one.
If 3, then try
DIMES
Since the score didn't change (using the above logic) when S -> M, M is not third.
if 2, then O is second because the only change from DOSES (not including S->M) was O->I and the score dropped and M cannot be third.
If 4 then I is second because the only change from DOSES to DIMES (not including S->M) was O->I and the score added one.