In this question, someone suggested using cream cheese to better replicate the effect of fresh mozzarella, milky and fatty. You likely won't want it by itself, but a little mixed in with your mozzarella or a few dabs scattered on top might give a nice richness. Or similarly adding fresh cheeses, like ricotta or cottage cheese, will also give a milky taste and add fats for a rich mouthfeel, and might complement your mozzarella nicely. Even a good feta has something to add in creaminess, the texture and taste - though I prefer the sheep's or goat's milk fetas, rather than the common low-fat variety.
On the other hand, these will also add moisture - so if you were going out of your way to find low-moisture mozzarella for a reason, then these additions might not be to your taste.
Another option might be to go back and get the full moisture mozzarella, and mix it with the low-moisture to see if you can get decent results that way. Overall, the results should be in between (depending on the precise mix) but it might give reasonable results.
Or you could do something with white sauce, possibly with other flavorings, garlic, herbs - maybe as your sauce base for the pizza, or else just pour a small amount in with your shredded cheese and toss well, and use the damp tangles on top of whatever other sauce yo would normally use. This can be a way to add all sorts of other flavorings, if you want, by incorporating them into the white sauce.
Or you could look into rich toppings for your pizza, to make up some of the flavor. I thought of oil-marinated olives, or vegetables roasted or sauteed in oil, or else something with its own fats like bacon, to get added flavor in with your fat. Adding pesto would fit in with these options, as well.
Basically, I would suggest make it less about adding fat for the sake of "making up for" the mozzarella, and more about adding richness and flavors to make something really tasty. You might find some recipes where this low-fat mozzarella works wonderfully, and yet the full-fat mozzarella might make the result too rich.