Can you explain what you mean by "meaty"?
If you mean tire section width or possibly tread width, you can fit tires at least as wide as 305 on 11" wide wheels if the wheels have the right offset. My road course track tires measure about 300mm wide on the rims they're fitted to and they neither rub anywhere nor poke out past the sheetmetal.
How wide are your wheels? That will define the maximum width tire you should consider mounting on them.
If you mean sidewall height or profile, you're throwing away a whole inch (about 10 profile points) by going to 20's over 18's. 255/40-20's run about the same height as 255/50-18's.
If you mean sidewall 'bulge', that's a matter involving wheel width - and there are limits on how far you should squeeze a tire down on rims too narrow for it just to make a low-profile tire look like it's 1960 all over again.
Norm