If I recall correctly, EMM386 would actually switch to protected mode an run DOS as a v86 application. It provided VCPI and DPMI apis. Their use case was a bit different (VCPI would allow you to run your code in ring0, while DPMI would run on ring2.

Fun fact, Win95/98 could of course run 32 bit DPMI apps without a problem, and many of the relevant OS interrupts such as 21h could be invoked directly from protected mode.