at most / possibly
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at most
Expresses an upper limit or a maximum possibility; in the sense of 'at most' or 'at best'.
Wir können allenfalls mit einer kleinen Entschädigung rechnen, mehr wird es nicht geben.
We can at most expect a small compensation; there won't be anything more.
The word is made up of 'allen' and 'Falls' (genitive of 'Fall'). Literally, it means 'in all cases', but it has developed the meaning 'at best' or 'at most'.
Die Reparatur wird allenfalls 100 Euro kosten.
The repair will cost at most 100 euros.
'Allenfalls' can stand at the beginning of a sentence (position 1), in which case the verb follows directly after it. It can also stand in the middle of the sentence, usually before the part that it limits.
Allenfalls könnten wir morgen anrufen.
At most, we could call tomorrow.
In the meaning of 'perhaps' or 'possibly', 'allenfalls' belongs to elevated written language. In normal conversation, it is rarely used in this sense.
Man könnte allenfalls einwenden, dass die Zeit zu knapp war.
One could possibly object that there was too little time.
maybe
'vielleicht' and 'allenfalls' can both express that something is only possible and not certain. 'vielleicht' is the normal everyday word and fits open possibilities. 'allenfalls' sounds more elevated and is less common. Very often, it does not simply mean 'maybe', but sets a limit: at most or at best. So 'allenfalls' is more precise when you want to say that no more should be expected. For normal uncertainty, 'vielleicht' is usually more natural.
Wegen des kleinen Raums können allenfalls zwanzig Personen an der Veranstaltung teilnehmen.
Because of the small room, at most twenty people can attend the event.
Vielleicht bleibt meine Nachbarin wegen des Wetters heute zu Hause.
Maybe my neighbor is staying home today because of the weather.