Question

1. We also had science lessons *with famous scientists*.

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Does "with famous scientists" modify 'science lessons'?
If "we" are the other lecturers and they were supposed to teach students together "with famous scientists", can "with famous scientists" modify 'had'?

Answer 1

"Does "with famous scientists" modify 'science lessons'?"

yes
This sentence also reads as if "we" are the students.
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If you want "with famous scientists" to modify "had," then it needs to be closer to that verb in the sentence. Here's how I'd phrase such a sentence:

Along with famous scientists, we taught science lessons.