Personally, I create a single angle from the spine to the cutting edge, then I create a bevel at whatever angle I need for the type of work I do with that particular knife,
This is more or less how I sharpen many of my knives. But the "single angle" is usually more of a thin convex. You can't often get a true full flat grind without over-thinning the meat behind the edge, unless ur talking bout a delicate straight razor or a knife with a really thick spine. Although with chromium-free steel, you can get really, really thin, as long as you don't mind some folding of the edge, now and then.
It's fun sharpening a knife with a distinct bevel, on occasion. It is good to keep up the skill. But most of my hard-working knives, and especially knives with a recurve, I like to reduce edge bevel to nothing or close to it. It makes them that much easier to maintain. I almost can't wait to ruin the edge, haha.
The other problem with the initial thinning of a high carbide knife is.... the scratches. Oh, boy. Removing the scratches from a high carbide knife steel can waste the entire afternoon! I think that we old-school carbon steel guys are more likely to favor the thin edge, small bevel/microbevel strategy. Not to mention, a lot of the premium knives people put in their pockets come with brushed finish or some surface coating, and erasing the bevel would scar up the looks.
I do NOT like sharpening the 340 stainless blades on pocket knives. Gimme carbon steel anyday! Not only does the stainless not hold an edge like carbon steel, it's a real pain to put a keen edge on with my stones. I found out why years ago...stroking the edge across the stones results in a tiny "curl" to the cutting edge. Best I can do is strop it when I'm done to remove it.
I think if you were to look close enough, all steels form a bur off a rigid stone. Some worse than others. Sure 'nuff, you can reduce the bur to almost nothing off a nice smooth stone and a light touch, particularly if you raise the angle just slightly on the last stroke.* But under a microscope, there is going to be some small bur, there. I often use an edge straight off the stone, particularly in the kitchen. But if I am near a strop, I will more than likely finish on it just to know the bur is gone.
*By just slightly, I mean the opposite, actually. Raising a GOOD amount but using feather light pressure on a fine hone for just a stroke or 3. This will remove the bur (but raise a very tiny new one, theoretically), in case you don't have a strop handy. Some would call this putting a microbevel on the knife. I just call it sharpening without a strop. As much as you want to think the edge on your knife is perfect, it is not. Well-formed edge = sharp and durable edge. I learnt to stop obsessing over thin apex angle. If you don't finish it on strop or by this "microbevel" method, it will have an extra degree of toothy, tomato slicing sharpness, but it won't last. Even a single cut in a piece of paper could turn the bur.
If you're unlucky, the only good rock you will find is in 500 lb pieces. If you have a generator and a hammer drill, you might want to bring them along. 
