Hang with me here. I know Nintendo would never go for this, but in a perfect world…
Nintendo should license Xbox live for Switch. For those of us that are cross platform gamers, it would be great. Imagine me getting on my xbox to play Halo, and I see that you are playing Mario Kart. I shoot you an invite, then hop on my switch and join you. We battle it out in some mario kart(you probably kick my butt) then i see my cousin is playing Halo, so I turn my Xbox back on and join him.
It would help Nintendo immensely due to the fact that Xbox live has had a great formula for years, it would also help 3rd parties because they would only have to deal with 1 platform to get their games running on 2 platforms.
The options in the market place would only show what games are available for the system you are logged in on.
Microsoft has said in the past that they are willing to work with other console companies, and I think it would be wise for both companies to treat eachother as compliments to eachother than competitors. It would also help Microsoft become more of a household name in Japan.
They could split profits by time logged in per system.