```ts
export function applyOverrides(
  base: Record<string, string>,
  overrides: string[],
): Record<string, string> {
  if (!Array.isArray(overrides)) {
    throw new Error("overrides must be an array");
  }

  const merged = { ...base };

  for (const override of overrides) {
    const parts = override.split(/=(.+)/);
    if (parts.length !== 2) {
      throw new Error(`invalid override: ${override}`);
    }
    const [name, value] = parts;
    if (!name || !base.hasOwnProperty(name)) {
      throw new Error(`invalid override name: ${name}`);
    }
    merged[name] = value;
  }

  return merged;
}
```