Use a grout colorant.

What kind of grout is it?

Can you show us? Sometimes things turn out to be lucky accidents. A darker grout on the floor might workout better.

If it's a small bathroom, once a rug is down, it won't be as noticeable.

Don't rush yet.

Simple answer to your question, is no, grout cannot be added over the top of grout. The old grout needs to come out 100%.

"Simple answer to your question, is no, grout cannot be added over the top of grout. The old grout needs to come out 100%."

That's not true, it depends what type of grout it is. Single component and epoxy grouts can be added on top of the same type grout. Cementitious grout can be added if 2/3 of the depth of the grout is first removed.

Refer to the manufacturer of the grout. Too many variables and the evolution of grout technologies. Personally, I'd never add grout on top of grout but refer to the manufacturer and your professional installer.