I have a bunch of the shapeoko essential clamps, that I have used paired with double sided carpet tape. These work wonderfully for hardwoods and I usually cut 1/2" or bigger material. But, I have been needing to cut some 1/4" plywood and I struggle getting the thin (and often warped) material to lay flat. The clamps don’t get tight enough for the thin material.
Are there any tricks or suggestions for holding thinner materials?
Yep what Tex said. Also on some brands of plywood even the blue painters tape will pull small splinters of the top veneer up especially if it is really thin.