Would a Noahide be allowed to add or subtract from the seven laws of Noah?
Rambam says in Melachim uMilchamot - Chapter 8 (11)
Anyone who accepts upon himself the fulfillment of these seven mitzvot and is precise in their observance is considered one of 'the pious among the gentiles' and will merit a share in the world to come.
This applies only when he accepts them and fulfills them because the Holy One, blessed be He, commanded them in the Torah and informed us through Moses, our teacher, that Noah's descendants had been commanded to fulfill them previously.
However, if he fulfills them out of intellectual conviction, he is not a resident alien, nor of 'the pious among the gentiles,' nor of their wise men.
It can therefore be deduced that any changes he makes out of his own thoughts will not attract the rewards associated with the 7 Noahide laws. He may think he has made changes but the results of the changes will not be the same as the Noahide laws.
According to Sefer Sheva Mitsvos Hashem vol I, Perek 3 (which deals with the prohibition of creating a new religion) they are forbidden both to add or subtract. The "adding laws scenario" would imply, of course, one to know exactly which laws are derivations or subdivisions of its own legislation and not merely additions to a particular law instead.
The Rambam in Hilchot Melachim 10:9 writes:
The general principle governing these matters is: They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions. They may either become righteous converts and accept all the mitzvot or retain their statutes without adding or detracting from them.
However, in the next halacha, the Rambam writes:
We should not prevent a gentile who desires to perform one of the Torah's mitzvot in order to receive reward from doing so, provided he performs it as required. If he brings an animal to be sacrificed as a burnt offering, we should receive it.
If a gentile who observes the seven mitzvot gives charity, we should accept it from him.
According to R. Moshe Feinstein, when the Rambam writes that a gentile may perform one of the Torah's mitzvot, he refers only to mitzvot such as charity which we find gentiles fulfilling in Tanach, but not other mitzvot. R. Moshe bases his position in part on the first halacha quoted herein. However, in a responsum the Rambam clearly does not hold this distinction (see here). The Beiur Halacha too (end of 304) writes that a ger toshav can accept additional mitzvot. Although the Rambam writes that a Noahide may not add to his mitzvot, there may be a difference between "adding" and volunteering.