verbs - Can there be such a thing as のんでましょう？

I know のみましょう but I was wondering if the above was legal japanese as well.

Answer

When in doubt, as someone Japanese, or else search for the exact word or phrase to see if it appears in Japanese blogs, forum discussions, online publications or other material.

There are a million hits for 飲んでましょう, in quotes, and 0.8 million more for 飲んでいましょう. So the evidence points to the answer that it is "valid" in the sense that it is in reasonably wide use by the people.

Reading some of these, it is difficult to see if there is any difference in meaning or distinguishing usage.

You would think that the progressive + volitional form would emphasize the ongoing activity. Let's do this, and keep going: let's be doing this.

This is making me curious.

A good pair to research　may be 遊んで（い）ましょう　vs. 遊びましょう. This would reveal if one is a preferred way to say "let's play regularly" versus "let's play now". I'm thinking that people would express this more often than "let's drink all the time". :)

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Update from asking Japanese speaker, shedding some additional light.

This progressive volitional is appropriate if the activity is already going on. If people are already drinking (飲んでいる) then it makes for one of them to say もっと飲んでいましょう (let's drink more; let's keep drinking).

This applies to －たい (want to do).

今「遊んでいる」、だから　｢もっと遊んでたい。/もっと遊んでいましょう。」

今「遊んでない」、だから　｢遊びたい。/遊びましょう。」