If you look at your micronutrient makeup of your food at somewhere like nutritiondata.com (they have a huge breakdown) you can see if you're lacking something and change accordingly. But overall, it has more to do with if you're getting everything you need, not necessarily variety for variety sake. Variety will likely be easier to randomly get all your nutrients, but if you pick the right mix of foods, you'd still get that and not have to eat an "everything under the sun" sampler.
A good multi can fill in your gaps, and maybe a quality supplement vitamin or mineral if you're really not eating something (like vegans will often have to supplement B vitamins).
So first look at what you eat. You're prolly not gonna have huge deficiencies by nature of eating meat, but it's not a guarantee.
