So what's the biggest width I could go without a change
Again, it's not width or wheel size, it's outside diameter (height). Google "tire size calculator". Enter your current size and then the width and wheel size you want and it will tell you what tire to buy and keep the same OD.
1989 Blue LX Hatchback
2001 Red SVT Cobra Convertible (Phoenix)
2002 Black/Red GT (Ginger)
2011 Red Candy Metallic V6 (Manfred)
2016 Magnetic Metallic GT (Susie II)