@Todd Ziegler -- I need to contribute info that's contrary to your thoughts.

I apologize!
Yes, it is possible to blend synthetic detergents (syndets) with true lye-based soap (a detergent that can be made by "natural" means).
In the industry, these cleansers are called "combars". Many commercial products are combars; Dove being one example. The advantages of a combar over pure soap or pure syndet --
Soap is less expensive than syndets, so including soap => product that is cheaper to make
Soap doesn't clean or lather well in hard water, syndets aren't affected by hard water
A blend of detergents tends to be milder to the skin than a single detergent
I haven't tried adding syndets to bar soap (yet). I've played around with adding small amounts of syndets (under 5% by weight) to liquid soap and found this works fine. No weirdness except some syndets will thicken liquid soap and some don't. I haven't tried syndets in bar soap yet, but others have. There have been the occasional thread about adding syndets to bar soap. Here are two I know of --
I have nearly a pound of Sodium Lauryl Sulfoacetate and I was wondering if I can add it to CP at trace? I'm concerned about how it will react with the lye and water that are present at trace. Since my slsa is powder form, it gets wet and foamy very easy. Figured I would mix it with oil and...
www.soapmakingforum.com
I didn't want to hijack the Solid Dish Detergent thread even more, but the idea that came up there sounds intriguing to me. Has anyone experimented much with hybrid soap bars -- lye based soaps that contain synthetic detergents? What was your experience? Is it worth it at all? -- E.g., is the...
www.soapmakingforum.com
edit-- Soap is anionic (negatively charged), and you don't want to mix soap with a cationic surfactant (positively charged). One familiar example of a cationic surfactant is BTMS emulsifier. Every once in awhile people ask about mixing BTMS into soap -- it's not recommended.
Anionic detergents that are compatible with soap include sodium lauryl sulfate (SLS), sodium laureth sulfate (SLeS), sodium lauryl sulfoacetate (SLS), sodium cocoyl isethionate (SCI), and sodium C14-C16 Olefin sulfonate (Bioterge).
Polysorbate 80 (PS80) is non-ionic, and cocamidopropyl betaine (CAPB) is amphoteric. --end edit
If you sell soap, be advised a combar is not considered true soap and you cannot sell it under the minimal regs for true lye-based soap. The labeling for a combar has to conform to the FDA rules for cosmetics.