〜でも（例示）

Here でも picks one typical example out of several possibilities without insisting on it, which softens invitations, suggestions and offers: 「お茶でも飲みませんか」. It leaves the listener free to choose something else, so it sounds more polite than naming the thing directly with を. Don't confuse it with the 'even ~' meaning (子どもでもできる) or with the concessive 〜ても.

• コーヒーでも飲みませんか。

  コーヒーでものみませんか。

  Would you like to have a coffee or something?

• 日曜日は映画でも見に行こうか。

  にちようびはえいがでもみにいこうか。

  Shall we go see a movie or something on Sunday?

• 疲れたでしょう。少し休んで、お菓子でもどうぞ。

  つかれたでしょう。すこしやすんで、おかしでもどうぞ。

  You must be tired. Take a rest and have some sweets or something.