In the records of the American Expeditionary Force (A.E.F) in the First World War, the abbreviation "S.O.S" customarily stands for Services of Supply.
There is a helpful List of Abbreviations and Military Terms used by the A.E.F which you might find helpful in your further research.
As noted in the Wikipedia page, the Services of Supply had:
"hospitals able to handle 35,000 sick and wounded."
Volume 15 of United States Army in the World War 1917-1919: Reports of the Commander-in-Chief, Staff Sections and Services includes some further detail.
In the section titled The Replacement System of the A. E. F. it states:
The first General Order on the subject (G. 0.46. G. H. Q .. March 26. 1918. contained Provisional Orders Governing Replacement of Personnel. the salient features of
Officers and soldiers of combat organizations to be dropped from rolls upon
evacuation to S. O. S. hospitals; and upon recovery to be returned to their organization
from hospital direct to Replacement Division.
It is this process to which the term "trans to S.O.S." generally refers, although in cases of wounded personnel I have more commonly seen it appear as "trans to S.O.S. hospital".
Note that in the case of British, Canadian, Australian and New Zealand service personnel the term "S.O.S" on the muster roll meant "Struck off Strength", and would commonly be followed by the reason (e.g. transferred to hospital, desertion, etc.).