All three words, más, mucho and muy, are adverbs of quantity. The only difference between them is that, while más and mucho can stand alone, muy always requires an adjective or adverb after it.
más and mucho can be followed by another word, but there are cases when they don't need it:
Por más que te esfuerces, no lo lograrás. (Even if you try (hard), you won't make it.)
(más + noun) Por más esfuerzos que hagas, no lo lograrás. (No matter how many efforts you make, you won't make it.)
(más + adjective) Por más trabajador que seas, no lo lograrás. (No matter how hard-working you are, you won't make it.)
(más + adverb) Por más duro que trabajes, no lo lograrás. (No matter how hard you work, you won't make it.)
Por mucho que te esfuerces, no lo lograrás. (Even if you try hard, you won't make it.)
(mucho + noun) Por mucho esfuerzo que hagas, no lo lograrás. (No matter how much effort you make, you won't make it.)
muy always requires another word after it:
(muy + adjective) Por muy trabajador que seas, no lo lograrás. (No matter how hard-working you are, you won't make it.)
(muy + adverb) Por muy duro que trabajes, no lo lograrás. (No matter how hard you work, you won't make it.)
As regards the mood, I agree with @pablodf76 that "por más" also accepts indicative. The subjunctive is far more usual than the indicative, which is only used when whatever is contained in the concessive clause is taken as a fact. The subjunctive, however, will tend to be used at all times when the verb in the main clause points to a subsequent time. Notice that, if present indicative is used in the subordinate clause, present will also be used in the main one:
- Por más que te esfuerzas, no cubres mis expectativas. (Even though you try (hard), you don't meet my expectations.)