You can go for a more muted version of your primary color in order to solidify your branding. This will require a white or grey overlay on the background in order for text to show up.
Alternatively, you could just have the whole website be an off-white color, which is the more common choice. It’s inoffensive, and won’t stop anything – text, images, or links – from jumping off the page.
Look no further than our own website to see what a blank, gray background can highlight.