Beefy is good only as long as the wheels are wide enough for the tire size. Keep in mind that pinching a tire down to fit it on a too-narrow wheel will actually draw the sidewalls in and make it narrower. Really.
Something like what W.O.T. posted is good.
275/40's on OE 18x8's is not, and even 255/45's on those same 8's is on the verge of being not OK.
I'm with Norm on this one, your tires need to fit the wheels properly or you are, at best, wasting extra money on a bigger tire that doesn't fully contact the ground. Far too many mustang people squeeze tires that are too big onto smaller wheels.
Some of the advice happening in here is mind blowingly wrong. A staggered car will not handle better. You'll understeer at the limit. You'll burn through tires more often (yes you really will, there's a reason Michelin halves their tire warranty if you do staggered sizes). You'll sacrifice braking grip if you have good enough brakes to engage ABS...
If you aren't buying wheels, simply buy the largest tire that will -correctly- fit (8 - 235, 8.5 - 245, 9 - 255, 9.5 - 265-275, 10, 275-285, etc.). If you have all the same size wheels, get all the same size tires.