Most of the attention in a colourful room goes to the colour. What actually holds it together is quieter than that.
A neutral base is the foundation, but a base is not only paint. It is the rug underfoot, the weight of a lamp on a side table, the texture of a bowl you keep on the dining table whether or not anyone is coming over.
Texture before pattern
Natural fibre does the work that paint cannot. A woven rug, a rattan stool, a raffia shade. These read as neutral from across the room but hold interest up close, which is what keeps a restrained palette from going flat.
Lighting is furniture
A table lamp is one of the few things in a room at eye level when you are seated. It is worth choosing like a piece of furniture rather than a utility. In an island house, where the doors are open and the light changes all day, lamps also decide what the room feels like after dark.
Things that are used
Island rooms are not for looking at. The pieces that make them work are the ones that get picked up. Bowls that hold fruit, napkins that go on the table, art you chose because you liked it rather than because it matched.
Start neutral, build texture, then let colour be the loudest thing in the room. It usually is anyway.