First, consider that brown people can usually wear the whole spectrum of warm-toned neutrals from coffee-brown through chocolate and khaki to barely-there eggshell. Some can wear black or white, but don't bet on it. Instead, use the darkest brown and lightest ivory as warmed-up black and white. Warm-toned grays and gray-browns also work, of which taupe is a great example though often hard to find. Among near-neutrals, rust is a brighter shade of orange-brown that often works. But navy rarely looks good on brown skin, and olive is tricky. If you know the tricks, like keeping difficult colors away from your skin (as on a belt) then you can actually wear any color; but that's a more advanced skill that not everyone wants to mess with.
As an interesting quirk, brown people often look fabulous in neons and super-saturated colors that look terrible on fair skin with cool tones. While this isn't a first thought for most business wardrobes, they make great accent colors when set against a neutral background. Think how often you've seen black ladies with screaming pink fingernails or black men with brilliant ties. So one very useful strategy for this kind of office wardrobe is to buy most of it in neutrals, then add clusters of several very bright accents.
If you want more color, consider an African tribal palette. These deep, rich colors are just slightly offset from the rainbow versions. They match the earthy tones of the African landscape and people. They're as ubiquitous there as the cool colors are in northern Europe or America. These colors are easy to wear as larger garments. Plus if you like tribal prints, you can get things to match and wear those on the weekends, using your same core neutrals.
Another way to dress up neutrals is to use patterns. Animal prints can be bold and striking, or relatively subtle. Brightly colored versions also exist, useful as accents. Geometric patterns and colorblocking also work.
Let's look at some examples.
A Core of Four has two tops and two bottoms. Here are some in dark brown, fawn, buff, khaki, and beige. Here is a complete 4x4 wardrobe in shades of brown.
The Common Wardrobe uses a different set of basics. Here is a warm one with burgundy and fawn accents. This one for cool weather leans casual. Consider accents like peach, lime, ivory, or amber.
Whatever's Clean 13 is a wardrobe you can't clash. These examples for men show warm and cool weather.
This wardrobe uses shades of brown and orange, plus accessories. This one uses brown and red. Here is a dressy combination of buff and cream.
Consider clusters of accessories in Amethyst Rose, Aurora Red, Cadmium Orange, Marsala, Meadowlark, Nile Green, or Spicy Mustard.
Here's a dressy capsule wardrobe using leopard prints in shades of brown and tan. This one adds bright pops of color like you might see at an office holiday party.
So if you have some shade of brown skin, don't get frustrated with the cool palette generally presented as "business colors." Find colors that look good on you.