You could use a Modify Player effect to modify the catalog for the unit but that would affect all instances of that unit.
Last I checked it was much worse to modify data than it was to use buffs due to a resource leak. Each time data is modified it made a duplicate of that data leaving the previous copy in memory, unused. Thanks to efficient algorithms it did not slow the game down but it did mean exiting the game could take several minutes due to some inefficiency with freeing the extra allocated copies. Additionally if several million such modifications were made it is possible some clients may crash due to out of memory errors.
I recommend looking at how Rexar does this for his one trait in Heroes of the Storm. He might use a method compatible with Heroes of the Storm. I suspect it was done with stacking buffs.