HELP! CL55 AMG Wheels and Tyres !!

I have a CL55 AMG - late 2002 (facelift). Its the 215 series. It's quite simply, the best car I've ever driven in my entire life!
I currently have the standard 5 spoke AMG 19" alloys. The back tyres are 275 / 35 / 19 / ZR and the front tyres are 245 / 40 / 19 / ZR.
My question is quite simply this. Without actually changing my alloys what is the biggest tyre size I can put onto the existing wheels? I'm getting mixed stories and would really value an answer by someone that knows their stuff!
I look forward to hearing from someone soon !



