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If someone has fulfilled an obligation (like kiddush), can he then do it for others?

I had been under the impression that somebody who is not personally obligated in a *mitzvah* (or maybe specifically a *b'racha*?) cannot do it on behalf of someone else.  This is one of the usual explanations for why a woman can't lead (most) prayer in mixed groups, for example -- she's not obligated so men who are obligated can't fulfill that obligation through her.  My question isn't about women and prayer; that's just background for why I thought the general rule is as I said.

I have heard an unsourced claim that this isn't necessarily true for *kiddush* -- that somebody can make *kiddush* and then make it again on behalf of others.  I'm not asking about cases where people merely *help others* fulfill a commandment, such as by guiding them through putting on *t'fillin* or waving the *lulav*.  I'm asking about cases where someone is fulfilling an obligation through someone else.

When can someone who has already fulfilled an obligation repeat the action so that somebody else can fulfill it through him?  Is the distinction not about whether you've *fulfilled* it but whether you were *obligated*, and somebody could in principle make *kiddush*, or say the *amidah*, or count the *omer* many times in a single day for different listeners?