Is there any way to set up a game to play online with another player; where the game would start from a desired position in order to play and study with the other player?

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sure, go to start game on your online chess page and look in advanced options where by default it says standard position. Just scroll down to whatever you want.

Thanks; but I'm talking about setting up a game previously played by one of the players that we could look at from a desired position in that game and try different ideas from that point.

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You can play the desired opening as far as it'll let you, and hopefully your friend will play the rest correctly.

I don't think this exact feature exists yet (i.e. to set up a position of choice and the plan from it), but it's something to think about for the future.  You could just play an unrated take-back game and play out the game to a desired point?