Can anyone suggest a way to get cupcakes to rise higher, creating more of a domed top? Might it just be a matter of filling the cupcake tins higher, or maybe something can be added to the mix?
Add baking powder, or more baking powder if there’s already baking powder in it.
Or you could just put more mix in the cups, but you’ll have to adjust the baking time as well.
If “domed top” is what you’re looking for, I’d go with the baking powder. It’ll add more oomph to the rise.
Breads of all kinds rise because of the action of a leavening agent. Yeast, for example, is a microorganism that converts sugars in the dough to carbon dioxide, which form little pockets of space. As the dough is baked, the heat sets it and the pockets of air remain, which is what makes bread look like it does.
Baking powder does the same thing – it’s a mixture of sodium bicarbonate and salt, which don’t react with each other when dry. But when wet, they react and emit carbon dioxide gas. Same effect – the dough rises.
Yeast adds a certain taste; baking powder is more generally taste-neutral. If your muffins won’t benefit from the yeast flavor, try baking powder.
But there’s a caution to baking powder as well. If you have excessive salt, acidity, in the mixture to begin with, your acids will react with the sodium bicarbonate and leave portions of the baking powder’s acids in the food, which can create an unpleasant taste. You would solve this problem by using baking soda alone – just the sodium bicarbonate.
So – leavening. Yeast, baking powder, baking soda.
But if there’s not enough acid in the rest of the ingredients, the baking soda won’t create a rise. That’s why I didn’t include it in my list; without seeing the actual recipe the OP is using, it’s impossible to say if baking soda would do anything.
Ok, very good – we’re going to be doing some experimental batches, so we’ll play around with these suggestions.
Mixing up the stuff in the pre-packaged cake mix box. 
Correct, which was the reason for the subjunctive mood in my sentence *If you have excessive salt, acidity, in the mixture to begin with, your acids will react with the sodium bicarbonate and leave portions of the baking powder’s acids in the food, which can create an unpleasant taste. * If you don’t, this is not applicable.