A quote from "A valency dictionary of English" (Herbst et al. 2004: 25), with some modifications:

A. Agree can mean 'be of the same opinion'

(i) People can agree on or about a particular topic or issue.

(ii) A person can agree with another person on or about a particular topic or issue.

(iii) A person can agree that something is the case.

B. Agree can mean 'consent'.

(i) A person or organisation can agree to or with something suggested.

(ii) A person or organisation can agree to do something suggested.

C. If two statements or versions of something agree, they are the same; if figures or calculations agree, they show the same result. Grammatical categories also agree, i.e. correspond in number etc.

D. Agree can mean 'come to a common conclusion'.

(i) People can agree some course of action, i.e. decide upon it.

(ii) People can agree on something as the result of a discussion.

(iii) People can agree to do something.

E. If something such as food or the climate does not agree with a person, it causes them problems.