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1) Shall we meet for a drink? (Still a common expression in Canada and the UK. It sounds more formal and business-like)) 2) Can you meet me for a drink later? (Using CAN stresses their ability to come, perhaps because they have finished work) 3) Would you like to have a drink with me? ( Using WOULD sounds positive and inviting)

Very close! We rarely use 'shall' in everyday spoken American English, however, it is used when we are trying to sound fancy or sarcastic. 1. Would you like to meet for a drink? 2. Correct! 3. Doesn't make sense, use sentence #1. I would say: Wouldn't it be awesome if we got a drink together?!