According to the help:
Is it possible to make the button execute two actions?
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Button["Click Here", Print[10!]; Print[11!]]
when clicked it performs two actions
CompoundExpression, which will be more familiar in the form of the
; operator (which many wouldn't recognize as an operator at all).
This works anywhere where a single command seems to be called for in a syntax description.
CompoundExpression returns the result of the last operation or
Null if there isn't any.