Not familiar with the Diamond travel vouchers but I know you can do this with other vouchers that have the same T&Cs (bump vouchers). You should be able to do it online if just you but if that fails you can definitely do this by calling in.
I have done this three times in the past 6 months combining bump vouchers (had a $1000 and then a separate $500 from the same trip, both in my name). One time1 with 2 passengers (me + fiancee) on a PNR and two times when it was just me on the PNR and had these three experiences as a DL Silver:
Me + Fiancee: Had to call to combine, wasn't able to combine online but no problem with manual rate desk
Just Me
#1 : Was able to combine online
Just Me
#2 : Had to call in to combine, wasn't able to combine online but no problem with manual rate desk