Decorating with three colours is a way to get a more dynamic look than two colours. At the same time, making sure that you have three colours that go well together can be stressful. For example, sage and burgundy are already complementary colours; they are colours that are opposite each other on the colour wheel. When together, these colours intensify each other. You can add a third colour to this decorating scheme, but it should be located on an area of the colour wheel that will cause the locations of the red, green and third colour to make a triangle.
Royal blue is directly opposite red and green and thus complements sage green and burgundy. The royal blue harmoniously blends well with the sage green as they're both cool colours. At the same time, the richness of the royal blue would go well with the rich shade of red present in the burgundy, giving the entire room an elegant atmosphere.
Rose or mauve
Rose and mauve are pinkish colours with a degree of dustiness or mutedness that gives them a certain versatility when combining them with other colours. Rose and mauve are both warm colours like burgundy. At the same time, rose and mauve are both lighter blends of pink, just as sage green is a lighter shade of green. The rose and the mauve would gracefully contrast the sage green.
Orange is opposite red and green on the colour wheel and directly across from blue. Because orange is a natural complement to green and red, copper will go well with sage green and burgundy as copper is just a metallic, more burnished shade of orange. Copper is inherently a warm colour like burgundy, yet at the same time has such a striking contrast to a colour like sage green that they both stand out against each other. The shimmery tones of copper will give a room a fancier look, yet not as fancy and formal as gold.