The answer is yes, no and maybe - the answer being dependent on whether one takes an empirical or philosophical perspective.
Empirically laws do change. Although its commonly taken that Newon discovered gravity, in fact everyone does, its so obvious that it geneally doesn't usually warrant the name of a law. Aristotle had a dual nature of gravity where celestial objects moved in circles and terrestial objects moved in striaght lines towards the centre of the earth. Newtons discovery can then be put in perspective as seeing that these two separate phenomena where aspects of one force. Hence Universal gravity. But there was a lacuna in his theory - how was force transmitted at a distance? Einstein fixed this by showing gravity was curvature of spacetime. He discovered this by pondering on the fixed speed of light which went against Galilean mechanics. This fixed speed of light is seen as one of the fundamental fixed constants of physics. But some physicists have speculated that the speed is not constant always, close to the big bang they have considered how & why it might change - this being a proposal to explain some cosmological features whose standard explanation is inflation.
Philosophically, that is metaphysically, that is after or before physics - one can consider whether the true laws of physics - the ones that physics aim at - are they fixed or not. This is a tricky question. First the laws may be fixed but our descriptions of them may vary. Secondly they may be fixed but we may never know this - since there is no reason per se that new laws come into existence at higher and higher energies. Perhaps there is a law whose effect is only apparent at energies close to the big bang.
For this reason physicists generally talk about laws upto a certain energy.
Further, taking a Kantian perspective, or correlationist in some contemporary discourse, the laws of nature as understood or intuited by us are within only the phenomenal realm; in the noumenal realm, it exists as the phenomenal world supervenes on it, but it itself is indescribable, having no attributes we can ever hope to have purchase on. If one then considers nature in its proper sense to be both this world of phenomena and the world of noumena then one can say that the larger part of nature is forever out of reach.
Or one can take a Spinozan perspective. If God exists as the solely neccessary self-subsistent sunstance, and the world is his creation, then supposing nothing can come from nohing, the world itself is a part of God, for this Spinoza was denounced as a Pantheist; further he said that God had an infinite number of modes, with only two being cognisant by us - extension and thought. So again when world is considered as a whole, the larger part of the world, that is God, is beyond us.
An Islamic perspective take all laws to be fixed by God except for human beings who are endowed with free will to make ethical choices. So all laws of nature at bottom until revoked by God are at bottom fixed. One could suppose that God could unfix these laws, but this goes against the spirit of what is meant by Nature here. The world of natural phenomena in the world.