"BobS" suggested:

... consider using some dowels to add some strength
to this pieces you add. You could also cut a M&T joint
along the top edges then glue the top pieces on. The M&T
joint will give it strength.

To which "Guy LaRochelle" replied...

The rear jaw is 1.5" thick and the front jaw is 3" thick. I don't know how
useful dowels would be since the piece I would laminate on top would only
be
about 3/8" thick at most to bring the jaw flush with the bench top.

No matter the thickness ( 1/4", 3/8", whatever ), I agree that the dowels
(or M&T) will add to the shear strength of the jaw caps. If you should have
the need to clamp just the bottom 1/4" of a workpiece at the top of your
vise, this strength may be appreciated.

/rick.