You may. This shampoo for blonde hair, however, was specifically designed to improve the appearance, shine, and texture of highly damaged or over-processed blonde hair. If someone who is brunette or red used this product, they would see colour-preserving, smoothing, shine, and fiber-alignment benefits but it has not been optimized to improve brunette/red colour.
 
We recommend that brunettes use Brilliant Brunette^® Multi-Tone Revealing Moisturizing products, which have been optimized for the needs of brunette colour-treated hair. We recommend that colour-treated reds use Radiant Red^® Colour Protecting Shampoo and Conditioner, which have been optimized to meet the needs of red colour-treated hair.