Custom search box as a fragment

[Buzby]

Is there any way you could have a custom search box as a fragment that already has one word fixed, and allows only the 2nd word to be entered.

For instace you sell widgets by Brand1 and brand2.

On brand1 search when you enter RED it will only show red widgets by brand1

and

On brand2 search it will only show red widgets by brand2

If this makes sense.

Many thanks

Jason