
mehrfach
repeatedly
Several times; happening repeatedly at different points in time.
Ich habe dich mehrfach angerufen, aber du bist nicht rangegangen.
I called you repeatedly, but you didn't pick up.
repeatedly / multiple
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repeatedly
Several times; happening repeatedly at different points in time.
Ich habe dich mehrfach angerufen, aber du bist nicht rangegangen.
I called you repeatedly, but you didn't pick up.

multiple
Present in more than one version or copy; counting more than once.
Der Sportler ist bereits mehrfacher Weltmeister.
The athlete is already a multiple world champion.
The word is made up of 'mehr' (more) and the ending '-fach'. The ending '-fach' means '-times' or '-fold' and is also used in other number words such as 'einfach' (single/simple), 'zweifach' (double/twofold), or 'vielfach' (many times/multiple).
Bitte drucken Sie das Dokument in dreifacher Ausführung.
Please print the document in triplicate.
'Mehrfach' can be used as an adverb or an adjective. As an adverb, meaning 'several times', it is not declined. As an adjective, meaning 'present more than once', it comes before a noun and is declined.
Er hat mehrfach versucht, sie zu erreichen.
He tried repeatedly to reach her.
As an adjective, 'mehrfach' (multiple) is often used in connection with titles, awards, or copies. Typical examples are 'mehrfacher Sieger' (multiple winner), 'mehrfache Preisträgerin' (multiple award winner), or 'in mehrfacher Ausfertigung' (in multiple copies).
Der Vertrag muss in mehrfacher Ausfertigung unterschrieben werden.
The contract must be signed in multiple copies.
several times
Mehrfach and mehrmals can both express a repeated action. Mehrmals tends to emphasize several occasions, while mehrfach can more strongly highlight repeated execution or the number of repetitions. For an action performed at different points in time, mehrmals is therefore especially suitable; when the number of repetitions is emphasized, mehrfach is the more natural choice.

Ich habe die Nachricht mehrfach gelesen, um kein wichtiges Detail zu übersehen.
I read the message repeatedly so that I wouldn't miss any important detail.
Ich habe die Nachricht mehrmals an verschiedenen Tagen gelesen.
I read the message several times on different days.