here is the issue, the plywood because of the underlying glue line, as well as the glue is absorbed somewhat into the veneer, thus very little penetration is afforded, and penetration is what carries the color to the wood, since you cannot change this you have to change the solid wood , by applying a coat of either 50/50 waterbased finish/water to the solid wood ( always test sometimes two coats are needed) or a coat of natural waterbased finish like general finishes natural, you reduce the absorbitive properties of the solid wood,the key is to get them balanced, now the problem becomes that your stain probably will not give you the color you want because its not able to penetrate, if its an oil base stain, it is going to also seal the wood as it stains, we all know a second coat of oil based stain doesnt do alot, thats why, if it were me, i would look to a good quality waterbased stain, water based stains do not seal the wood like oil, and act much like a dye, good crisp grain definition and you can apply several coats and actually get a deeper color, water base is also compatable under all finishes when its dry which it does very fast, now not wanting to sound like a commerical for General finishes , but their waterbase stain is very heavy bodied, and act almost like a gel , so it colors well on the surface which is what you need, and retains very good clarity, I have tried the box store water based and its ..well lets just say..not the same …hope this helps
