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We are using the thrie beam transition to rigid barrier developed in TRP-03-210-10.    This transition was crash tested without a curb under it.  Some other thrie beam transitions that MwRSF has crash tested used a sloped 4-inch curb.

Is it possible to use a 4" sloped curb similar to the previous crash tests with the transition in TRP-03-210-10?

I am assuming that you are referring to the curb detailed in TRP-03-69-98.  If so, I do not believe that the addition of the 4" sloped curb would cause any adverse effects.  However, be sure to use the same geometry for the curb, i.e., the height, slope, and length of the curb should not exceed that dimensions illustrated in the noted report.  Note, this will keep your curb downstream of the asymmetrical transition piece and within the thrie beam rail sections for the newer transition.  Further, the lateral placement of the curb must be as detailed in the original report (with the back of the curb adjacent to the face of the post).