There have been a few studies looking specifically into this type of thing. The problem is that consumption of red meat tends to be correlated with poor diet, e.g., people who eat a lot of fast food end up eating a lot of meat, and very little fiber, lots of saturated fat, etc.
I remember hearing of a study that split people into tertiles of low, medium, high meat consumption and low, medium, high vegetable consumption, and the conclusion was that in people who consume a lot of veggies (who generally have a good diet) do not experience any negative effects of high meat consumption. I can't find the exact study, but I did find a study that seems similar (looks at meat consumption while controlling for diet quality using the HEI), and the one I'm thinking of is probably from the same lab.