If you are willing to change the system, and slow down suggestions, you can have it in string search suggestions:
Modify the tsysDBobjects table, for the row where DBobjName = 'web50Quicksearch' and change the Query value so that the first expression of (tblAssets.AssetName LIKE @q) replace the @q with @qf. Note that the Query value contains single quotes so you must double them up to use an Update SQL expression when updating the table something like:
UPDATE [tsysDBobjects]
SET [query] = '<new query>'
WHERE DBobjName = 'web50Quicksearch'
where <new query> is the existing value copied out and modified so the first @q is changed to @qf.
Works pretty fast on our system.
PS You can add an interior wildcard character (I used asterisk) by replacing all the @qf in the query with REPLACE(@qf, '*', '%') - don't forget to double up single quotes if using a SQL update to do this.
PPS If you don't update web50fullsearch similarly, the quicksearch page (when you press enter) won't give the same results as the suggestions.