There are multitasking options using DESQview(/X) or Windows >=3.1. A friend of mine in high school ran a 4 line BBS using DESQview and 4 Courier 28.8K modems.

In real mode, it's possible to have a TSR that swaps the entire contents of RAM from disk. As long as such a hypothetical TSR is always loaded into a fixed location, it's possible to save and restore the entire DOS, program, and/or EMS/XMS session.