DR DOS, at least version 6 or later (Novell DOS, DR OpenDOS etc.), provides an uninstallation option: the installer preserves the current boot sector and system files, and DR DOS can then be uninstalled (using the
UNINSTAL command) and the system restored to its initial state. DR DOS also supports alternate
CONFIG.SYS files (
DCONFIG.SYS) which can be used to support multi-booting, with some extra effort (I can’t remember the details off-hand).
The installer can be started in a number of ways, either by booting from the installation floppy, or starting the setup program from MS-DOS. It’s a wizard-style installer, with built-in help.
I would suggest trying the latest available version of OpenDOS 7¹ if you want to go down this route. DR DOS is highly compatible with MS-DOS: the official interfaces are supported as-is, and many undocumented interfaces are handled as well.
However, as far as multi-tasking goes there are a couple of important caveats in your situation. DR DOS does have built-in task-switching and multi-tasking (using the “Task Manager”, or TaskMAX in earlier versions), but multi-tasking requires a 386, and task-switching with OpenDOS 7 on a 286 requires 3MiB of memory. Earlier versions of DR DOS (5.0 and 6.0), using TaskMAX, swap tasks to disk by default, and should work on your system as long as you have enough disk space for the swap file.
¹ DR DOS 8 no longer includes the task manager. As far as version 7 goes, 7.01 got third-party enhancements (notably, FAT32 support) which might not be relevant on a 286 with a small hard drive; later versions don’t have these improvements.