My eldest daughter's Bas Mitzvah parsha included the issurim of bal tigra (do not deduct from a mitzvah) and bal tosif (do no add onto a mitzvah). As Rashi explains, this means that one should not do things like have three or five parshios in one's t'filllin; one should not have three or five species in one's lulav bundle; and so forth. Subtracting from the mitzvah is clearly wrong; in fact, it is so wrong one wonders why there needs to be an issur for it. On the other hand, what's wrong with adding another parsha to t'fillin or adding another kind of tree/fruit to the arba minim; it's got what you need, plus more. Together we came up with a nice mashal.
My daughter likes baking, and the idea is azoi. You might think it is ok to leave out part of a mitzvah; after all, you are at least getting partial credit, right? Think about baking a cake. Leave out one ingredient, say, for example, flour; that's not a partial cake, that's not a cake at all. On the other hand, add one ingredient, such as, for example, concrete; that's not cake plus, that's not a cake at all. So too, adding to or subtracting from a mitzvah results in something that just is not a mitzvah at all. To save you from fooling yourself into thinking you were doing either partial or extra credit, the Torah forbade the behavior.
That being the case, how do we have a concept of hiddur mitzvah? That's an especially hot topic now, with Chanuka just around the corner. Chanuka is not just hiddur mitzvah time, the minhag has actually become that everyone lights according to the m'hadrin min ha'm'hadrin version!
The essential difference is that the very definition of the mitzvah of t'fillin is to have four parshios. The very definition of the mitzvah of the lulav bundle is to have four species. Chanuka licht are not the essential mitzvah -- even though the bracha is "l'hadlik ner shel chanuka". The mitzvah is really pirsuma nisa -- publicizing the miracle that HaShem performed for us. The bracha really means that Chazal commanded us to light chanuka lights in fulfillment of the mitzvah to publicize the miracles HaShem has done for us. It's too many words, so the bracha just gives the headline. Since lighting candles is not the mitzvah, but the way to express the underlying mitzvah, lighting more candles does that even better.
Where are you going to find the mitzvah of prisuma nisa? It's one dimension of "v'ahavta es HaShem Elokecha"; part of expressing love is shouting from the roof tops, or from the window sill, in this case.