more: to a greater degree, more intensely, or in greater measure than before or than something else
TranslatabilityDirectCertaintySettled
This is the plain comparative force of the word: something happens to a greater extent, or one thing outweighs another in measure. It can sharpen a verb (people grew quiet, and then grew quiet still more), strengthen a comparison (you matter more than the birds), or push a quantity higher (faith and love kept growing more and more).
A distinct and very common shade of this same degree sense is the from-the-lesser-to-the-greater argument: if something is already true in a smaller case, then how much more must it be true in the greater one. Greek marks this with the word paired with "how much" or "by much" (poso mallon, pollo mallon). The logic is the same comparison of measure, now used as a step in reasoning, so the senses below sit together under one core idea of greater degree.
The two shades are kept separate only because the second has a recognizable rhetorical job (building an argument from the small to the great), while the first simply raises the level of whatever is being described.
Nuances
1ato a greater degree; more intensely or in greater measure
rather: in preference to something else, instead of it, or as the better choice
TranslatabilityDirectCertaintySettled
Here the word is not measuring how much, but choosing between options. It sets one thing over another and says: this one, not that one. English usually says rather or instead.
The choice can be a correction (you should rather have mourned), a priority (go instead to the lost sheep; obey God rather than people), or a contrast of loves and values (they loved the darkness rather than the light; lovers of pleasure rather than lovers of God). In many of these the word stands beside a small word meaning than, naming the option that is being set aside.
This preference sense grows naturally out of the degree sense: to want something more is a short step from wanting it instead. But the everyday force is different enough that translators reach for a different English word, which is why it is treated as its own meaning.
covers both raising a degree and choosing one option over another, so the same Greek word can also mean "rather" or "instead" where English "more" would misleadJhn 3:19
Both
both name a greater degree or measure of somethingAct 9:221Th 4:10
Only more
English "more" is almost always heard as a question of quantity or degree, not as choosing instead of something
the same word elsewhere simply intensifies a degree ("more"), so "rather" fits only where a choice between options is in viewRom 5:9
Both
both set one option over another as the preferred choiceAct 5:291Co 6:7
Only rather
English "rather" can drift into a soft "somewhat" or "quite," which this word never means
“instead”
Comparison data is not available for this English gloss yet.
How mallon differs from similar Greek words
μάλισταthe top step of the same family: not just more but most of all, especially, above all; where mallon raises the level or picks one option, malista singles out the foremost case.
Sets two named things side by side and takes one, refusing the other. Peter and the apostles obey God and not people; the crowd loves the darkness and not the light.Act 5:29Act 4:19Jhn 3:19Jhn 12:432Ti 3:4Heb 11:25
Redirects behavior, usually rendered "instead" or "rather": stop the thing you are doing and do this other thing. The thief is to work, the church is to grieve, the believer is to accept the wrong done to him.Eph 4:28Eph 5:111Co 6:71Co 5:2Rom 14:13Mat 10:6
Turns up something already under way, so that pressure, opposition, or a closing deadline only raises the pitch: the crowd spreads the news all the harder, the blind man shouts louder, the meeting matters more as the Day draws near.Mrk 7:36Mrk 10:48Jhn 5:18Act 5:14Heb 10:252Pe 1:10
Carries the step of an argument from a smaller certainty to a larger one, in the pattern "if that much is already true, how much more this". It is the backbone of Jesus on the grass of the field and of Paul on being saved by the life of Christ.Mat 6:30Mat 7:11Rom 5:9Heb 9:14Heb 12:9
Reports an outcome that ran the opposite way from the effort spent on it: the woman spent everything on doctors and only got worse, Pilate got a riot instead of a settlement.Mrk 5:26Mat 27:24
Both
Both raise one thing above what surrounds it, so a single sentence can stack them. Paul calls the runaway slave a dear brother, above all to himself, and then asks how much more he must be to Philemon.Phm 1:16
Neither word counts anything; both rank. Paul does not say how many believers God saves or how many parts of the body are needed, only which stands higher, so a translation that drops the word loses the emphasis without losing the facts.1Ti 4:101Co 12:22
Lifts one part of a group that has just been named without pushing the rest aside. The whole group stays in view and one slice of it is brought forward: good to everyone, and above all to the family of faith; Savior of all people, and above all of believers.Gal 6:101Ti 4:101Ti 5:81Ti 5:17Php 4:22
Names the worst offenders inside a warning, telling the reader who the writer chiefly has in mind while leaving the warning itself wider than that group.Tit 1:102Pe 2:10
Heads the strongest reason for a request, or picks out the one hearer who matters most among those present.Act 26:3Act 25:26
Marks which item weighed heaviest when several are in play at once: the parchments above the rest of the books, one sentence above everything else that made the elders grieve.2Ti 4:13Act 20:38
What scholars say about mallon
BDAG treats mallon under two heads: a marker of degree ("more, to a greater degree," including the emphatic comparative and the a fortiori poso/pollo mallon "how much more") and a marker of preference ("rather, sooner, instead"), the latter frequently with a following e ("than"). The form is the comparative adverb of mala, with the superlative malista ("most of all, especially"). The degree and preference uses are continuous rather than two unrelated words: a heightened degree shades into preference. Standard grammars (BDF) note the construction with e and the elliptical comparative idioms.
Sources
BDAG, s.v. μᾶλλονlexicon
F. Blass, A. Debrunner, R. W. Funk, A Greek Grammar of the New Testament (BDF), §§ 244, 246grammar
H. G. Liddell, R. Scott, H. S. Jones, A Greek-English Lexicon (LSJ), s.v. μάλα / μᾶλλονlexicon