1) Your child can do better with a different teacher.
2) Your child may do better with a different teacher.
3) Your child could do better with a different teacher.
4) Your child might do better with a different teacher.
Are they all correct/natural? (especially the first one)
Your child can do better with a different teacher
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Newton
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Alan
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Re: Your child can do better with a different teacher
Meaningful/plausible, except #1 ("can" is not synonymous with "may").