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Owing to her outstanding performance as a student, Kelly's phone had started ringing with job opportunities a month before she completed her doctoral degree.

Hi,

Does "with" in the above mean "because of" or something else? Thanks.
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It means the people who were calling her were calling with job opportunities as their topic to discuss with her.
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Thanks, GG.

But I'm still unsure of its meaning. Is it similar in meaning to the "with" in the following?

The ground was covered with snow.

The bag is filled with water.
No, those are far more literal meanings of with.

She called with good news = She called in the possession of good news that she wanted to share.

She's coming with an offer you won't be able to refuse = She is coming and will be making you an offer you can't turn down.

The phone rang with job offers = The people who called had job offers for her