1）shall用于第一、三人称的一般疑问句中（Shall I/we/he…?），表示征求对方的“建议”。
例句
a. Shall I open the window?
要不要我把窗子打开？
b. Shall we leave at two?
我们两点钟走如何？
c. Shall he come with us?
要不要他和我们一起去？
2）could在有些情况下并不表示过去能做某事，而是表示提议，也可以用can，但could没有can那么肯定。
—What shall we do this evening?
—We could go to the cinema.
3）may/might (just) as well 也常用来向他人推荐更佳方案，意为“倒不如……；不妨……”，如：
a. We may as well stay here tonight.
我们今晚不如在这儿过夜。
b. —I’ll go on Monday by train.
—You might just as well wait till Wednesday and go by plane.
4）其他非情态动词表示建议，如Let’s…，Why don’t…?，Why not…?等。
a. Let’s go to a movie.
b. Why don’t we go on a picnic?
忠告与建议的比较：should表示强烈的、明确的忠告。could表示委婉的建议。
例句
a. A: John doesn’t feel good. He has a bad stomachache.
B: He should see a doctor.
C: Well, he could see a doctor. Or he could simply stay in bed for a day and hope he feels better tomorrow.
b. A: I need to get to the airport.
B: You should take the airport bus. It’s cheaper than a taxi.
C: Well, you could take the airport bus. Or you could take a taxi. Maybe Clint could take you. He has a car.