If you really want to make your own, I have nothing to offer. If, on the other hand, you're willing to buy one, here are a few possibilities:
4"X9-3/4" TOOL MAKER'S PRECISION SCREWLESS VISE - NEW. JAW WIDTH: 4". JAW OPENING: 5". Jaw height: 1-7/8". HARDENED AND PRECISION GROUND.
www.ebay.com
JAW WIDTH: 4". JAW OPENING: 4-1/2". HARDENED AND PRECISION GROUND.
www.ebay.com
I checked Little Machine Shop (my usual "go to" source) but they only go up to 3"
CDCO has one for $105. Their website is
http://www.cdcotools.com Enter "vise" in the search box. The 4 incher is stock number 21124
Shars sells one, stock #202-1233:
https://www.shars.com/4-x-4-7-8-precision-toolmakers-vise
They even have a 5 incher!