You have a lot of wood there ,I wouldn't paint the whole ceiling dark but rather like this one

White Brick Mediterranean · More Info

The color of this wood ceiling below would be more typical for a Spanish style home. Painting the ceiling chocolate would be WAY TOO DARK. Could you consider removing some of the current finish on the ceiling?

A taupewash would be OK also.

Yes, but be aware the chocolate beams will really draw your eye up.

Depends on how dominant you want this to be... All of the above suggestions are good :)

You have great design taste, I would suggest only painting the beams if you have your heart set on painting anything; I think it looks great as it is. IT looks like your fireplace is painted, would you consider changing it up with a bright accent color? Also, I love how you put your plants on top of your shelving...great idea.

When we repainted our interior we had all the ceilings match the walls, ( a light tan) with just a bit of white added. And I hate it. The ceilings feel too heavy. And some of my rooms have tall ceilings without beams, but still feel heavy and dark. Use caution to not make the ceiling feel darker than the walls.

My honest opinion is ,the ceiling is very nice and it also has a lot of wood beams ,if you were to paint them in a brown it would look too busy ,keep it one colour only ,I would say yes if you only had a few beams to paint,just like the ideas that I posted above.