Are both sentences correct?
(a) I suggested that she go there with me.
(b) I suggested that she would go there with me.
My theory is like this:
(a) means: I said to her, “Would you like to go there with me?”
(b) means: I said (implicitly) to someone, “She will go there with me.”
(a) is correct and means what you say. Without context, (b) may at first appear to be incorrect. I suppose it is theoretically possible in the context that you describe, but it seems an unusual combination, probably one that is hardly ever used in practice.
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(a) is correct and means what you say. Without context, (b) may at first appear to be incorrect. I suppose it is theoretically possible in the context that you describe, but it seems an unusual combination, probably one that is hardly ever used in practice.
Koji from Japan(b) I suggested that she would go there with me.
The more common modal (British English) is "should."
Although "would" is possible, I can't remember that I have ever used it this way.