You could it just becomes heavier. I've used foil to good effect but am having a stainless steel plate made that would double as a grill plate when I need to do that sort of cooking, to sit on the top as a more permanent solution. A local steel company can do the laster cutting for me and it is a reasonable price.
Today's lunch cooked on the Kettle pizza with foil layer on second deck: Proscuitto & Buffalo Mozzarella. No particular science to the dough, I just use high gluten bread flour, add some yeast, let it rise, knock it back, make some dough balls and let them rise a bit again before making the pizzas.
I removed the hinged portions of the grille and I can slip in wood and push it to the back to re-fuel. The trick to the kettle pizza is to control the wood flame, you can get it too hot, and you can easily burn the pizzas. With a foiled or fully covered top deck, I can cook a 90 sec pizza, and again if you are not careful with the fire, you can burn it in 2 1/2 mins. The Kettle pizza gets up to temp for me in about 20 mins, and I only ever make a max of four to six pies when we have guests, normally 2 or 3 when it is just our family. It does not need insulation, it is designed to get up to the temp, and cook a pizza quickly - so what I do now is to get to close 400 deg C and then I spike the temp with kindling to raise it to about 450 or thereabouts. Slip the pizza in , and with one turn its done. The WF is what makes this contraption work. Frankly I have cooked without wood splits and have used just kindling, it works - the Kettlepizza is not a WF hearth with a long burning fire, it is a WF cooker, - it heats up quicker than a regular WFO and offers you that short window of heat conditions to cook like a WFO when you have it up to desired temp.